Elliptic $G$-operators on manifolds with isolated singularities

We study elliptic operators on manifolds with singularities such that a discrete group $G$ acts on the manifold. Following the standard elliptic theory approach, we define the Fredholm property of an operator by its principal symbol. For this problem, we prove that the symbol is a pair consisting of the symbol on the principal stratum (the inner symbol) and the symbol at the conical point (the conormal symbol). We establish the Fredholm property of elliptic elements.