FIDE are doing their own investigation, but the chess.com cheat detection algorithm is apparently well regarded, and online cheating is obviously very simple to do. He's admitted cheating online as recently as 3 years ago. If he can reasonably be proved to having cheated online more often and more recently than he has admitted to, then that gives good reason to suspect he'll have cheated OTB too given the chance.
There are various ways one might cheat OTB, from taking one's phone the bathroom in the middle of a tournament (some allow this!!), to getting signals from an accomplice who is seeing the game in real time. Signals could be electronic to some device on the player, or visual from an audience member in the room. It's been proposed to introduce a 15-30 min broadcast delay in tournament games as one way to prevent cheating. Some tournaments scan the players for electronic devices - not sure how foolproof this is.
There are various ways one might cheat OTB, from taking one's phone the bathroom in the middle of a tournament (some allow this!!), to getting signals from an accomplice who is seeing the game in real time. Signals could be electronic to some device on the player, or visual from an audience member in the room. It's been proposed to introduce a 15-30 min broadcast delay in tournament games as one way to prevent cheating. Some tournaments scan the players for electronic devices - not sure how foolproof this is.