Geodesic
Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary
Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 122-129

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Given an action of a discrete group $G$ on a smooth compact manifold $M$ with a boundary, we consider a class of operators generated by pseudodifferential operators on $M$ and shift operators associated with the group action. For elliptic operators in this class, we obtain a classification up to stable homotopies and show that the group of stable homotopy classes of such problems is isomorphic to the $K$-group of the crossed product of the algebra of continuous functions on the cotangent bundle over the interior of the manifold and the group $G$ acting on this algebra by automorphisms.
Keywords: elliptic operator, $K$-theory, crossed product, $G$-operator.
Mots-clés : homotopy classification 
@article{UFA_2016_8_3_a10,
     author = {A. Yu. Savin and B. Yu. Sternin},
     title = {Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary},
     journal = {Ufa mathematical journal},
     pages = {122--129},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2016_8_3_a10/}
}
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A. Yu. Savin; B. Yu. Sternin. Homotopy classification of elliptic problems associated with discrete group actions on manifolds with boundary. Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 122-129. http://geodesic.mathdoc.fr/item/UFA_2016_8_3_a10/