Inertia Orbifolds, Configuration Spaces and the Ghost Loop Space

In this paper we define and study the ghost loop orbifold LsX of an orbifold X consisting of those loops that remain constant in the coarse moduli space of X. We construct a configuration space model for LsX using an idea of G. Segal. From this we exhibit the relation between the Hochschild and cyclic homologies of the inertia orbifold of X (that generate the so‐called twisted sectors in string theory) and the ordinary and equivariant homologies of LsX. We also show how this clarifies the relation between Chen–Ruan orbifold cohomology, Hochschild homology, and periodic cyclic homology.