  In this paper, we prove that, over an algebraically closed field of odd
characteristic, a weakly tame automorphism of a K3 surface of finite height can
be lifted over the ring of Witt vectors of the base field. Also we prove that a
non-symplectic tame automorphism of a supersingular K3 surface or a symplectic
tame automorphism of a supersingular K3 surface of Artin-invariant at least 2
can be lifted over the ring of Witt vectors. Using these results, we prove, for
a weakly tame K3 surface of finite height, there is a lifting over the ring of
Witt vectors to which whole the automorphism group of the K3 surface can be
lifted. Also we prove a K3 surface equipped with a purely non-symplectic
automorphism of a certain order is unique up to isomorphism.
