The authors generalize a construction of Connes by defining for an -bundle over smooth manifold and a reduced cyclic cohomology class a sequence of de Rham cohomology classes . Here is a convenient algebra, defined by the authors, and is a locally trivial bundle with standard fibre a right finitely generated projective -module and bounded -modules homomorphisms as transition functions.
@article{701565, title = {Characteristic classes for $A$-bundles}, booktitle = {Proceedings of the Winter School "Geometry and Physics"}, series = {GDML\_Books}, publisher = {Circolo Matematico di Palermo}, address = {Palermo}, year = {1996}, pages = {[57]-71}, mrnumber = {MR1396602}, zbl = {0856.57022}, url = {http://dml.mathdoc.fr/item/701565} }
Cap, Andreas; Schichl, Hermann. Characteristic classes for $A$-bundles, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books, (1996), pp. [57]-71. http://gdmltest.u-ga.fr/item/701565/