Definitely. Most "Russian" OC busts in Western Europe these days involve Georgians, Armenians and Kurds/Yezidis. Azeris (and Talysh) and Chechens largely seem to stick to Russia, except for a few extortion rings here and there. Chechen organized crime had its time in the limelight in the 90s. They're still around of course, but not as endemic as before. Every few years a small group of Chechen criminals are busted in Antwerp; last time it was for a scheme where someone bought diamonds from a guy connected to the Chechens after which the Chechens robbed them back. Blue collar rackets for the most part.
The "Russian mafia" in Antwerp in the 90's and early 2000's were mostly Jewish criminals from Georgia and Ukraine; the Ukrainians left and the notorious Georgian-Jewish families have gone legit (for the most part).

Dunno what the state is on the bratvas in Russia. You hear nothing about the 'almighty' Solntsevo. I suppose most of them went largely legit.