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The authors generalize a construction of Connes by defining for an $A$-bundle $E$ over smooth manifold $X$ and a reduced cyclic cohomology class $c$ a sequence of de Rham cohomology classes $ch_c^k (E)$. Here $A$ is a convenient algebra, defined by the authors, and $E$ is a locally trivial bundle with standard fibre a right finitely generated projective $A$-module and bounded $A$-modules homomorphisms as transition functions.
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