Title: The Baum-Connes Conjecture

The report below is a short account of past and recent work on a conjecture of P.~Baum and A.~Connes about the $K$-theory of group $C^*$-algebras.

1991 Mathematics Subject Classification: 96K56, 46L80

Keywords and Phrases: Baum-Connes conjecture, group $C^*$-algebras, $K$-theory.

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