We consider the assembly map for principal bundles with fiber a countable discrete group. obtain an index-theoretic interpretation of this homomorphism by providing tensor-product presentation module sections associated to Miščenko line bundle. In addition, we give proof Atiyah’s L2-index theorem in general context flat finitely generated projective Hilbert C∗-modules over compact Hausdorff spa...

In its original form, the Atiyah-Singer Index Theorem equates two global quantities of a closed manifold, one analytic (the index of an elliptic operator) and one topological (a characteristic number). Because it relates invariants from different branches of mathematics, the Index Theorem has many applications and extensions to differential geometry, K-theory, mathematical physics, and other fi...