The Tracial Class Property for Crossed Products by Finite Group Actions

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