MAYFIELD HEIGHTS, Ohio — Russian pop songs play in the background as immigrants browse the local deli for items they can rarely find outside their native Moscow: candies, dried salted fish, perogies, and heaps of imported sausage.

Some stop to pick up one of several Russian-language newspapers, which this week prominently feature coverage of Paul Manafort, the former campaign manager for Donald Trump whose consulting work for Russia’s allies in Ukraine has stirred controversy.

But lately what’s been happening in US politics is enough to cause them to choke on their $24-a-pound caviar. Their home country is once again caught in the glare of an American presidential contest, but this time through the lens of a funhouse mirror.

Four years ago, the former Republican nominee called Russia the “number one geopolitical foe.’’ Yet the current nominee, Donald Trump, is heaping lavish praise on Vladimir Putin — the strongman who invaded Crimea, is accused of killing political enemies, and is believed to be the driving force behind Russia’s hacking of Democratic Party computers.

In nearly two dozen interviews here — an area that has one of the greatest concentrations of Russians in the country — many said they were baffled by his Trump’s embrace of Putin. They want their former country and their current one to get along, but they grope for explanations for why Trump would so openly embrace the Russian president.

“I’m just surprised. Like, ‘Why? Why? Why?’ ’’ Tanya Chetyrkin, an accountant, said between sips of white wine after listening to a concert of Russian folk music.

Overall, the Russian-Americans expressed conflicting views about Putin and Trump. They are generally skeptical of those in power, but they also said they find comfort in strength and security. Most said they support Trump, remarking on his “strong’’ public profile.

But as for his support for Putin, and the spotlight it casts on Russia?

“It’s very surprising,’’ said Lena Kleiman, who moved here 25 years ago but hasn’t lost her thick Russian accent. “We’ve always been involved. But not this much.’’

Theories vary about Trump’s backing for Putin: “I think it was pulled in artificially by Trump,’’ Chetyrkin said. “He wants to be on the front page. ‘I will say Putin’s name and be on the front page and won’t have to pay for my ads.’ ’’

Ilona Bogen, a 38-year-old nurse who immigrated from Lithuania about 15 years ago and who is one of the few likely to support Hillary Clinton, said she has no idea why Trump is currying favor with Putin. “Those two are like dictators,’’ she added. “I’m really scared. . . . Putin and Trump, they would not be a good mixture.’’

While many are not excited about the choice of candidates, Trump’s perceived strength helped make him undeniably the first choice of those interviewed here.

“He’s strong. A leader is supposed to be strong . . . if it’s stronger, it’s better,’’ said Marius Shpaner, a 68-year-old retired engineer who moved here in 1990. “We talk about democracy. But after the election it’s a dictatorship, in any country. For four years it’s a dictatorship.’’

“This is important: He’s promised to protect us,’’ said his wife, Alexandra. “To be safe is most important.’’

Russians are decidedly not a key demographic in American elections, and only a sliver of the American population calls themselves Russian, either by birth or by ethnicity. Some fled Russia for political reasons during the Cold War, or were escaping religious persecution. Others past and present have migrated in search of economic prosperity and freedom.

Trump has upended the normal Republican approach to Russia. He recently went on a Russian television network. Manafort, his former campaign chairman, had ties in the region’s economy, as have some of his other advisers. Trump has said Putin is doing a “great job’’ and that he’s a better leader for Russia than Obama is for the United States.

“I think I’d get along very well with Vladimir Putin,’’ he said in July 2015.

Putin returned some of the praise in December 2015, calling Trump “brilliant.’’ (Although, as some Russians here noted, the phrase Putin used — yarkii — may be more precisely translated into “flamboyant’’ or “colorful.’’)

“It is always a great honor to be so nicely complimented by a man so highly respected within his own country and beyond,’’ Trump said in response.

Russia’s Interfax news agency reported last month that Russians overwhelmingly prefer Trump over Clinton. Some 35 percent said they believed he would be better for relations with Russia, while 13 percent preferred Clinton. Only 7 percent said they had a positive view of Obama.

Here in the Cleveland suburbs, most said they can’t take their eyes off this election. They are starting their days tuning their satellite dishes to Russian television, which is closely following Clinton’s health and doing stories on Trump’s family and his wealth. In side conversations at the Russian Orthodox churches or at the local grocery store or bar, the American election can feel inescapable.

Russia is accused of hacking into e-mails of Democratic campaign committees and prominent officials of both parties, including most recently former Secretary of State Colin Powell.

“It’s ridiculous! It’s funny. Russia coming up, that’s the biggest joke in this election,’’ said Boris Chetyrkin, a 68-year-old retiree. “They are trying to make us hate each other, and for what? It’s artificial.’’

At Restaurant Europa the other day, owner Alex Shneyder sat on a bar stool before showing off the “vodka room,’’ which has two deer heads inside a walk-in freezer, where customers are invited to step in to drink vodka after donning layers of fur.

“Russians support Trump. They like Trump,’’ said Shneyder, who is from Siberia and spent time in Moscow before moving here 26 years ago. “I know Trump is not the best man. But I don’t want a woman president.’’

Many don’t trust what they hear, either from politicians or from the media. They have seen no proof that Russia is behind the hacking.

“I think I can speak for all of us when I say: We’re tried of Russia being blamed for everything,’’ said Ala Abakumov, during a dinner at which Moscow Mules were served but a bottle of vodka went conspicuously unopened. “Some things are beyond the pale.’’

Most don’t really know what to make of Trump. Mention of his name can trigger eye rolls and laughter. They compliment his business acumen but they have a hard time figuring out his motives.

“He’s very impulsive,’’ said Roma Grinberg, who runs a Russian grocery store called Mayfield Fine Foods. “He’s like a wild horse. You never know what to expect from him.’’

Views on Putin are mixed. So Trump’s praise of Putin can be head-spinning for those who grew up under Soviet and Russian leaders.

“It’s a game, it’s not serious,’’ Shneyder said. “He’s not bringing Russian people. Russian people hate Putin. I don’t know why. It’s kind of strange.’’

Matt Viser can be reached at matt.viser@globe.com.