The Russian mafia is not limited to ethnic Russians, but to many nationalities from the former Soviet Union, most of which are now collectively known as the Commonwealth of Independent States. There are many stereotypes of the Russian mafia, including that it is dominated by Jews and Chechens.
Chechens indeed make up a disproportionate amount of Russian mafia members inside of Russia and Ukraine, and (arguably) Belarus. However, their presence is severely limited in other countries where the Russian mafia operates, notably the United States and Israel. Thus, while noticeable within the mafia's organization in Russia, Chechens play a small role in the Russian Mafia's overseas membership.
Russian Jews are also present in the Mafia structure, however the subject is complicated by several factors. First, more Jews are present in the Russian mafia's overseas operations than inside Russia because Russian Jews were more likely to successfully receive permission to emigrate the USSR via political refugee status. Second, despite Israel's Law of Return's explicit restriction of all immigrants (regardless of religion) with criminal implications from receiving citizenship, many Jewish Russian mobsters use evasive measures to still receive Israeli citizenship. Additionally, non-Jewish Russian mobsters often fraudulently claim Jewish ancestry in order to gain easier movement in and out of Israel (where the Russian Mafia has established a large operating base). Conversely, some Jews in the mafia either actively hide or do not acknowledge their Jewish background for various reasons. Finally, many ethnic Russians have partial Jewish ancestry, which they may or may not acknowledge. Because of these factors, it is difficult to determine the number of Jews in the Russian mafia. And while they by no means dominate the organization, a significant number of Russian mafia members do have Jewish roots.
The Russian Mafia also has a multitude of other nationalities such as Ukranians, Belarusians, Armenians, Moldovans, Khazaks, Uzbeks, Georgians, Dagestanis, Azeris, and others. Additionally, countries such as Armenia, Georgia, Ukraine, Estonia, Lithuania, Belarus, and Moldova have their own mafia organizations which have extensive links to the Russian mafia.
In the end, greed and ruthlessness counts for much more than one's nationality in the Russian mafia, whose bosses' main concern is profit, not politics.