$K$-homology of $C^*$-algebras

A functor algebraically dual to the operator $K$-functor is constructed on the category of $C^*$-algebras, and the author shows that it defines a homology theory on this category. The author also proves that it coincides with Kasparov's homology $K$-functor on a large class of $C^*$-algebras, including commutative $C^*$-algebras. This functor is used to describe a class of homotopy invariant higher signatures.
Bibliography: 10 titles.