AbstractWe give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of$K3$surfaces over finite fields. We prove that every$K3$surface of finite height over a finite field admits a characteristic$0$lifting whose generic fibre is a$K3$surface with complex multiplication. Combined with the results of Mukai and Buskin, we prove the Tate conjecture for the square of a$K3$surface over a finite field. To obtain these results, we construct an analogue of Kisin’s algebraic group for a$K3$surface of finite height and construct characteristic$0$liftings of the$K3$surface preserving the action of tori in the algebraic group. We obtain these results for$K3$surfaces over finite fields of any characteristics, including those of characteristic$2$or$3$.