  Given a group, we construct a fundamental additive functor on its orbit
category. We prove that any isomorphism conjecture valid for this fundamental
isomorphism functor holds for all additive functors, like K-theory, cyclic
homology, topological Hochschild homology, etc. Finally, we reduce this
fundamental isomorphism conjecture for K-theoretic ones.

K-Theory and Homology;Algebraic Topology