  In the present work we study elliptic operators on manifolds with
singularities in the situation, when the manifold is endowed with an action of
a discrete group $G$. As usual in elliptic theory, the Fredholm property of an
operator is governed by the properties of its principal symbol. We show that
the principal symbol in our situation is a pair, consisting of the symbol on
the main stratum (interior symbol) and the symbol at the conical point
(conormal symbol). Fredholm property of elliptic elements is obtained.
