Additivity of the rho map on the topological structure group

Let M be an orientable topological manifold of dimension m, m greater or equal to 5, with fundamental group $\mathrm{\Gamma }$. Let S(M) be the topological structure set, endowed with the group structure induced by its identification with Ranicki’s algebraic structure set. We prove that the (rationalized) rho map ${\rho }_{\mathrm{\Gamma }}:S(M)\to K_{m+1}(D_{\mathrm{\Gamma }}^{\ast })\otimes \mathbb{Q}$ is a homomorphism of abelian groups.