The Higson-Roe sequence for étale groupoids. I. Dual algebras and compatibility with the BC map

We introduce the dual Roe algebras for proper \'{e}tale groupoid actions and deduce the expected Higson-Roe short exact sequence. When the action is cocompact, we show that the Roe C^*-ideal of locally compact operators is Morita equivalent to the reduced C^*-algebra of our groupoid, and we further identify the boundary... Show more