Abstract
The verification of the isomorphism conjectures of Baum and Connes and Farrell and Jones for certain classes of groups is used to compute the algebraic K -a ndL-theory and the topolo- gicalK-theory of cocompact planar groups (D cocompact N.E.C-groups) and of groupsG appearing in an extension 1 ! Z n ! G ! ! 1w here is a finite group and the conjugation - action on Z n is free outside 0 2 Z n . These computations apply, for instance, to two-dimensional crystallographic groups and cocompact Fuchsian groups. Mathematics Subject Classifications ( 2000): 19B28, 19D50, 19G24, 19K99.
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