Hirshberg, Winter, and Zacharias introduced several versions of "higher dimensional Rokhlin properties". We prove, for example, that there is no action of any nontrivial finite group on the Jiang-Su algebra, and no action of Z / 3 Z on the 2^{\infty} UHF algebra, which has any higher dimensional Rokhlin property with commuting towers. The proof is based on the generalization to C*-algebras of the Atiyah-Segal Completion Theorem from topology.

This is joint work with Ilan Hirshberg.