The Tracial Class Property for Crossed Products by Finite Group Actions - Xinbing Yang; Xiaochun Fang (Abstract and Applied Analysis)
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 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 𝒞-algebra.