"Internet nexus of cultural Judaism" — Examiner.com
I think his father may be one of those "hidden Jews" (or maybe part-Jews) in Russia and Vladimir Kramnik may be at least part-Jewish on his father's side: 1) I know it may not mean much, but he definitely looks a lot more "Jewish" than "ethnic Russian".2) Wikipedia says his dad's original name was Sokolov, which sounds just as Jew-y as Kramnik (his stepfather Kramnik was almost certainly Jewish as it is a Jewish last name: http://www.eilatgordinlevitan.com/kurenets/k_pages/kramnik.html)Lots of Russian atheletes, etc. didn't know about their Jewish background until well after they were famous, just my thoughts. Granted, I couldn't find anything on the web to prove any Jewish background for him.
As Russian names go, Sokolov is pretty goyishe... Whether Kramnik was Jewish was a big question in Russia during his reign as champion, and there is absolutely no confirmation than he is -- other than the probably Jewish stepfather.