Geodesic
Elliptic $G$-operators on manifolds with isolated singularities
Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 173-191

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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. 
@article{CMFD_2016_59_a7,
     author = {A. Yu. Savin and B. Yu. Sternin},
     title = {Elliptic $G$-operators on manifolds with isolated singularities},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {173--191},
     publisher = {mathdoc},
     volume = {59},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2016_59_a7/}
}
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A. Yu. Savin; B. Yu. Sternin. Elliptic $G$-operators on manifolds with isolated singularities. Contemporary Mathematics. Fundamental Directions, Proceedings of the Seventh International Conference on Differential and Functional-Differential Equations (Moscow, August 22–29, 2014). Part 2, Tome 59 (2016), pp. 173-191. http://geodesic.mathdoc.fr/item/CMFD_2016_59_a7/