ISOMETRIC ACTIONS ARE QUASIDIAGONAL

Abstract

We show every isometric action of a countable discrete group on a compact space is quasidiagonal in a strong sense. This shows that reduced crossed products by such actions are quasidiagonal or MF whenever the reduced group $C^{\ast }$-algebra of the acting group is quasidiagonal or MF. We use this to show new examples of group actions whose crossed products are MF.