  We prove that every action of a finite group all of whose Sylow subgroups are
cyclic on the K-theory of a Kirchberg algebra can be lifted to an action on the
Kirchberg algebra. The proof uses a construction of Kirchberg algebras
generalizing the one of Cuntz-Krieger algebras, and a result on modules over
finite groups. As a corollary, every automorphism of the K-theory of a
Kirchberg algebra can be lifted to an automorphism of the Kirchberg algebra
with same order.
