In the context of algebraic K-theory, a classical question is whether for a group G the assembly map A(*) ? BG ? A(BG) is split injective. This talk aims to show that, in some cases, this result can be proven by establishing a corresponding decomposition of localizing motives for categories with G-action. I will explain that this method works under the assumption of Carlsson-Pedersen that appropriate equivariant compactifications of a model of EG exist. One can interpret this method as an analogue of the Gamma element method, which is used to prove split injectivity of the Baum-Connes assembly map. The talk is based on joint work with Georg Lehner.