Principal groupoid models for stable UCT Kirchberg algebras

Abstract

We show that every stable UCT Kirchberg algebra has a principal étale groupoid model, and thus contains a C${}^{\ast }$-diagonal. Every unital UCT Kirchberg algebra $A$ for which $[1_A{]}_0$ has infinite order in $K_0(A)$ is also covered by our methods. In particular, we obtain a principal étale groupoid model for the Cuntz algebra ${\mathcal{O}}_{\infty }$.

17 pages; submitted version