  We prove the following theorem: let $A$ be a UCT Kirchberg algebra, and let
$\alpha$ be a prime-order automorphism of $K_*(A)$, with $\alpha([1_A])=[1_A]$
in case $A$ is unital. Then $\alpha$ is induced from an automorphism of $A$
having the same order as $\alpha$. This result is extended to certain instances
of an equivariant inclusion of Kirchberg algebras. As a crucial ingredient we
prove the following result in representation theory: every module over the
integral group ring of a cyclic group of prime order has a natural presentation
by generalized lattices with no cyclotomic summands.
