Crossed products by finite group actions with certain tracial Rokhlin property

Abstract We introduce a special tracial Rokhlin property for unital C *-algebras. Let A be a unital tracial rank zero C *-algebra (or tracial rank no more than one C *-algebra). Suppose that α: G → Aut (A) is an action of a finite group G on A , which has this special tracial Rokhlin property, and suppose that A is a α-simple C *-algebra. Then, the crossed product C *-algebra C *( G, A ,α) has tracia rank zero (or has tracial rank no more than one). In fact, we get a more general results.