K-Theory for Partial Crossed Products by Discrete Groups

The notion of a partial crossed product of a C*-algebra by the group of integers introduced by R. Exel is generalized to a partial crossed product by any discrete group. A reduced partial crossed product is defined and some of the standard facts relating amenability and K-amenability to ordinary crossed products are extended to this case. The exact sequence of Pimsner and Voiculescu for reduced crossed products by the free group on n generators is generalized to this setting. This result is used to calculate the K-groups of an amalgamated product of two finite dimensional C*-algebras over a common maximal commutative subalgebra.