Generalized Twisted Sectors of Orbifolds

For a finitely generated discrete group Γ, the Γ-sectors of an orb-ifold Q are a disjoint union of orbifolds corresponding to homomorphisms from Γ into a groupoid presenting Q. Here, we show that the inertia orbifold and k-multi-sectors are special cases of the Γ-sectors, and that the Γ-sectors are orbifold covers of Leida's fixed-point sectors. In the case of a global quotient, we show that the Γ-sectors correspond to orbifolds considered by other authors for global quotient orbifolds as well as their direct generalization to the case of an orbifold given by a quotient by a Lie group. Furthermore, we develop a model for the Γ-sectors corresponding to a generalized loop space.