| Abstract: |
The purpose of this article is to develop in some detail the theory of equivariant asymptotic morphisms, appropriate to C*-algebras equipped with continuous
actions of locally compact groups, and so construct tools very similar to those
of Kasparov's equivariant KK-theory for calculating the K-theory of group
C*-algebras. A central problem in C*-algebra K-theory is the Baum-Connes con-
jecture, which proposes a formula for the K-theory of group C*-algebras. A
primary goal of the paper is to first formulate the conjecture in the language of
asymptotic morphisms, and then describe a general method, due essentially to
Kasparov, for attacking various cases of it. At present the method encompasses
nearly all that is known about the Baum-Connes conjecture.
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