The Solntsevskaya isn't really a 100% centralized organization. It's composed out of a ton of independently operating brigades with origins in Russia, Ukraine, Belarus, Moldova... (mostly ethnic Russian and Jewish criminals). The only thing which really ties them are their similar key money laundering contacts in Russia and the businessmen that provide them with the necessary political connections. There are often brigades feuding with one another.
Of course, the USA isn't really local territory for them so it's extremely difficult for them to penetrate politics in America. That's why they resort to strong-arm rackets and running scams in their own communities.
Solntsevskaya is not composed of independently running brigades. The group itself was formed in late 1980's in Moscow neighborhood Solncevo. Popular for those times the group absorbed and recruited smaller brigades under them, by good will or force. Such as in Latvia Valeriy "Tsigan(Gipsy)" Berlin said to be connected with most biggest crime group in Latvia - Kharitonov's Brigade, was killed due to refusing paying tax to Solncevskaya while being acting boss of the group. In other regions they either recruited other groups under them or sent there their own brigades to look over business. There is nothing independent in these groups which are under Solncevskaya - they are a big criminal network which relies on each other in different ways.
Their power goes more far, having Vory V Zakone on their side and even government officials, including the president himself. Not even speaking about that they own large businesses and even banks and other financial structures.
As in Solntsevskaya Bratva type groups . All the recent Russian OC busts in the States seem to involve small and relatively unsophisticated groups , as opposed to relatively large sophisticated ones that have important connections to the upperworld ( which is my personal definition of mafia style organized crime groups ) .
There are brigades operating from Solncevskaya and Izmailovskaya in the US, which are kind of mafia style groups but still with different structures and organizing than LCN.
As mentioned before, there is not that much of information available on these groups. I know some information, because I have loose connections to people who are involved with some groups or illegal businesses in my country. The small groups get arrested and prosecuted, the ones which are not so organized. Big groups like Solncevskaya are more smart, better investing and more reasonable. It's not the 90's anymore, when they needed to run around with guns and extort farmers selling tomatoes on the local market - that business now goes to small crews which are not smart. The big groups like Solncevskaya are more involved in financial crimes, such as fraud or large scale scams, not the typical LCN crimes which they make money on.
Speaking about media, @TheKillingJoke - Media is a business that runs on peoples attention. So they will make a sensation over everything. There is no doubt, that Russian groups are one of the most powerful in the world when it comes to business or eliminating their enemies. But I doubt that in US they are there to make danger to the average American unless they get involved in a bad way themselves. It's pretty logic - you fuck with criminals, they'll fuck you up, doesn't matter what ethnic they are. They are just there to make business, and mostly it's not violent one.
