2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75711In this paper we show that if a discrete group $G$ acts properly isometrically on a discrete space $X$ for which the uniform Roe algebra $C_u^*(X)$ is exact then $G$ is an exact group. As a corollary, we note that if the action is cocompact then the following are equivalent: The space $X$ has Yu's property A; $C^*_u(X)$ is exact; $C_u^*(X)$ is nuclear.5 pagesOperator AlgebrasFunctional AnalysisGroup Theory58B34; 20F69, 46L89text