The K-theory K_n(ℤG) and quadratic L-theory L_n(ℤG) functors provide information about the algebraic and geometric topology of a smooth manifold X with fundamental group G=π₁(X,x₀). Both K- and L-theory are difficult to compute in general and assembly maps give important information about these functors. Ranicki developed a combinatorial version of assembly by describing L-theory over additive bordism categories indexed over simplicial complexes. In this talk, I will present current work with Jim Davis where we define an equivariant version of Ranicki’s local / global assembly map and identify our local / global assembly map with the map on equivariant homology defined by Davis and Lück. I will also mention some applications of our results.