Generalized twisted sectors of orbifolds

For a finitely generated discrete group $Γ$, the $Γ$-sectors of an orbifold $Q$ 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.

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