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We introduce the dual Roe algebras for proper \'{e}tale groupoid actions anddeduce the expected Higson-Roe short exact sequence. When the action iscocompact, we show that the Roe $C^*$-ideal of locally compact operators isMorita equivalent to the reduced $C^*$-algebra of our groupoid, and we furtheridentify the boundary map of the associated periodic six-term exact sequencewith the Baum-Connes map, via a Paschke-Higson map for groupoids. For properactions on continuous families of manifolds of bounded geometry, we associatewith any $G$-equivariant Dirac-type family, a coarse index class whichgeneralizes the Paterson index class and also the Moore-Schochet Connes' indexclass for laminations.

The Higson-Roe sequence for \'{e}tale groupoids. I. Dual algebras and compatibility with the BC map