A periodicity theorem in the algebra of symbols

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.
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