2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75253Lie groupoids generalize transformation groups, and so provide a natural language for studying orbifolds and other noncommutative geometries. In this paper, we investigate a connection between orbifolds and equivariant stable homotopy theory using such groupoids. A different sort of twisted sector, along with a classical theorem of tom Dieck, allows for a natural definition of stable orbifold homotopy groups, and motivates defining extended unstable orbifold homotopy groups generalizing previous definitions.16 pages, no figuresAlgebraic Topology55P91 (Primary), 22A22 (Secondary)text