Let (A, R, α) be a C*-dynamical systerr, let H∞(α) be the subalgebra of A consisting of those a in A such that the Arveson spectrum of a is contained in [0, ∞), and let Aα be the fixed point subalgebra of A. In this note we investigate conditions for the existence of an R-invariant conditional expectation from A onto Aα and we show that when such an expectation exists, then the K-theory of H∞(α) is isomorphic to that of Aα. We show by example that if no such expectation exists, then the K-theories may be different.
