Do Ngoc Diep:
A survey of noncommutative geometry methods for Group Algebras
Journal of Lie Theory, vol. 3 (2), p.149-176
In this survey we shall report about a K-theoretic approach to study group
algebras. Following the example of the group of affine transformations of the
straight line, the method consists of: 1. Construction of irreducible group
representations (orbit method, category ${\cal O}$), 2. Decomposition of the
group algebra into a sequence of repeated extensions, and finally
3. Computation of the extension
invariants by the methods from noncommutative geometry (KK-theory,
cyclic theories).