2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70345Let G be a (not necessarily Hausdorff) locally compact groupoid. We introduce a notion of properness for G, which is invariant under Morita-equivalence. We show that any generalized morphism between two locally compact groupoids which satisfies some properness conditions induces a C*-correspondence from $C*_r(G_1)$ to $C^*_r(G_2)$, and thus two Morita equivalent groupoids have Morita-equivalent $C^*$-algebras.32 pages; short version; bibliographic references addedOperator AlgebrasK-Theory and Homology22A22 (Primary) 46L05, 46L80, 54D35 (Secondary)text