Finite group actions on C*-algebras with the Rohlin property, I

Abstract

Basic properties of finite group actions with the Rohlin property on unital C^*-algebras are investigated. A characterization of finite group actions with the Rohlin property on the Cuntz algebra ${\mathcal{0}}_2$ is given in terms of central sequences, which may be considered as an equivariant version of E. Kirchberg and N. C. Phillips's characterization of ${\mathcal{0}}_2$. A large class of symmetries on ${\mathcal{0}}_2$ are classified in terms of the fixed-point algebras for conjugacy and the crossed products for cocycle conjugacy. Model actions of symmetries of ${\mathcal{0}}_2$ are constructed for given K-theoretical invariants.