  For a finitely generated discrete group $\Gamma$, the $\Gamma$-sectors of an
orbifold $Q$ are a disjoint union of orbifolds corresponding to homomorphisms
from $\Gamma$ into a groupoid presenting $Q$. Here, we show that the inertia
orbifold and $k$-multi-sectors are special cases of the $\Gamma$-sectors, and
that the $\Gamma$-sectors are orbifold covers of Leida's fixed-point sectors.
In the case of a global quotient, we show that the $\Gamma$-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 $\Gamma$-sectors
corresponding to a generalized loop space.
