Differential groupoids and $C^*$-algebras

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The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.
41 pages, LaTex2e, 11 figures, use graphicx, psfrag, placeins, amssymbo, "supported by..." statement added, "fatal error" in Aknewledgment corrected, no other changes made

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