Symmetries of simple AT-algebras

Let A be a unital simple AT-algebra of real rank zero. Given an order two automorphism h : K1(A)-* K1(A), we show that there is an order two automorphism a: A-* A such that a*0 = id, a*1 = h and the action of Z2 generated by a has the tracial Rokhlin property. Consequently, C*(A, Z2, a) is a simple unital AH-algebra with no dimension growth, and with tracial rank zero. Thus, our main result can be considered the Z2-action analogue of the Lin-Osaka theorem. As a consequence, a positive answer to a lifting problem of Blackadar is also given for certain split case.