Compact group actions on UHF algebras obtained by folding the interval

Abstract

We show that for any integer p greater than one, there exists a C- ∗ algebra A , which is not AF, such that M p ∞⊗ A≃ M p ∞, where M p α = M p ⊗ ∞ is the UHF algebra of type p ∞. Using this construction of UHF algebras, as inductive limits of subhomogeneous algebras on an interval, embedded in each other via a folding operation on the interval, we exhibit actions of compact groups on UHF algebras whose fixed point algebras are not AF. In particular for any compact group G ≠ { e}, there exists an action of G on M p ∞ whose fixed point algebra is not AF.