Geodesic
A periodicity theorem in the algebra of symbols
Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 382-410 
B. V. Fedosov. A periodicity theorem in the algebra of symbols. Sbornik. Mathematics, Tome 34 (1978) no. 3, pp. 382-410. http://geodesic.mathdoc.fr/item/SM_1978_34_3_a6/
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     author = {B. V. Fedosov},
     title = {A~periodicity theorem in the algebra of symbols},
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     volume = {34},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1978_34_3_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce the concept of an elliptic family on the manifold $M$ in a trace algebra. We define the Chern character of an elliptic family. We also introduce the algebra of formal symbols on $\mathbf R^n$ with coefficients in a trace algebra. We establish a connection between the Chern characters of an elliptic family on $M$ in the algebra of formal symbols on $\mathbf R^n$ and of the elliptic family on $M\times\mathbf R^{2n}$ formed by the leading terms of the symbols. Bibliography: 8 titles.

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[8] M. A. Shubin, “Psevdodifferentsialnye pochti-periodicheskie operatory i algebry fon Neimana”, Trudy Mosk. matem. ob-va, XXXV (1976), 103–164