Non-cyclotomic Presentations of Modules and Prime-order Automorphisms of Kirchberg Algebras

We prove the following theorem: let A be a UCT Kirchberg algebra, and let α be a prime-order automorphism of K∗(A), with α([1A]) = [1A] in case A is unital. Then α is induced from an automorphism of A having the same order as α. 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.