Zappa-Szép product groupoids and C*-blends

Abstract

<p>We study the external and internal Zappa-Szép product of topological groupoids.We show that under natural continuity assumptions the Zappa-Szép product groupoid is étale if and only if the individual groupoids are étale. In our main result we show that the <i>C</i>*-algebra of a locally compact Hausdorff étale Zappa-Szép product groupoid is a <i>C</i>*-blend, in the sense of Exel, of the individual groupoid <i>C</i>*-algebras. We finish with some examples, including groupoids built from ⁎-commuting endomorphisms, and skew product groupoids.</p>