  We study the behavior of the Nil-subgroups of K-groups under localization. As
a consequence we obtain that the relative assembly map from the family of
finite subgroups to the family of virtually cyclic subgroups is rationally an
isomorphism. Combined with the equivariant Chern character we obtain a complete
computation of the rationalized source of the K-theoretic assembly map in terms
of group homology and the K-groups of finite cyclic subgroups.
