ON THE STRUCTURE OF SIMPLE C-STAR-ALGEBRAS TENSORED WITH A UHF-ALGEBRA

Let A be a simple unital C*-algebra and let B be a UHF-algebra. We prove that the group of invertible elements in A ⊗ B is dense in A ⊗ B if A is stably finite, and that A ⊗ B is purely infinite otherwise. We give (partial) results on the size of the closure of the group of invertible elements in more general simple unital C*-algebras. © 1991.