Trace acaling automorphisms of certain stable AF algebras II

Two automorphisms of a simple stable AF algebra with a finite dimensional lattice of lower semicontinuous traces are shown to be outer conjugate if they act in the same way on the K-group and the extremal traces are scaled by numbers which are not equal to 1 and satisfy a certain condition (which always holds if all the scaling factors are less than 1). The proof goes via the Rohlin property. As an application we consider the problem of classifying conjugacy or outer conjugacy classes of certain actions of the circle group on a separable purely infinite C*-algebra.