COMPACT GROUP-ACTIONS ON UHF ALGEBRAS OBTAINED BY FOLDING THE INTERVAL

We show that for any integer p greater than one, there exists a C-* algebra A, which is not AF, such that Mp∞⊗A≃Mp∞, where Mp = Mp⊗ ∞ 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 Mp whose fixed point algebra is not AF. © 1991.