The Tracial Class Property for Crossed Products by Finite Group Actions

We define the concept of tracial C-algebra of C*-algebras, which generalize the concept of local C-algebra of C*-algebras given by H. Osaka and N. C. Phillips. Let C be any class of separable unital C*-algebras. Let A be an infinite dimensional simple unital tracial C-algebra with the (SP)-property, and let alpha : G -> Aut(A) be an action of a finite group G on A which has the tracial Rokhlin property. Then A x(alpha) G is a simple unital tracial C-algebra.