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 be a prime-order automorphism of K_*(A), with ([1_A]) = [1_A] in case A is unital. Then is induced from an automorphism of A having the same order as . 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.