Abstract
We classify finite group actions on some classes of C ∗ -algebras with the Rohlin property in terms of the K-groups. A group cohomological obstruction is obtained for the K-groups of a C ∗ -algebra allowing such an action, for example, the Tate cohomology groups with the K-groups as the coefficient modules must vanish. Model actions with the Rohlin property are constructed for given K-theoretical invariants. Quasi-free actions of finite cyclic groups on the Cuntz algebras and their dual actions are investigated from the view point of the Rohlin property.
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