Abstract: For a finite group G, an object with a G-action in some semi-additive category, and any additive functor, there always exists a factorization square involving assembly, coassembly and norm maps. One can use this to give a completely formal proof that the assembly map in K- and L-theory for finite groups is rationally and K(n)-locally split-injective. I have some open conjectures for how one might deal with infinite groups as well.