Geodesic
On homotopic classification of elliptic problems with contractions and $K$-groups of corresponding $C^*$-algebras
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 64 (2018) no. 1, pp. 164-179

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We consider calculation of a group of stable homotopic classes for pseudodifferential elliptic boundary problems. We study this problem in terms of topological $K$-groups of some spaces in the following cases: for boundary-value problems on manifolds with boundaries, for conjugation problems with conditions on a closed submanifold of codimension one, and for nonlocal problems with contractions. 
@article{CMFD_2018_64_1_a9,
     author = {A. Yu. Savin},
     title = {On homotopic classification of elliptic problems with contractions and $K$-groups of corresponding $C^*$-algebras},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {164--179},
     publisher = {mathdoc},
     volume = {64},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2018_64_1_a9/}
}
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A. Yu. Savin. On homotopic classification of elliptic problems with contractions and $K$-groups of corresponding $C^*$-algebras. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 64 (2018) no. 1, pp. 164-179. http://geodesic.mathdoc.fr/item/CMFD_2018_64_1_a9/