By Kreck's modified surgery the question whether two closed, smooth, spin 4-manifolds M,M' with fundamental group G are stably diffeomorphic can be approached by computing the spin-bordism group of the classifying space BG. We study the situation where the fundamental group of M is that of an closed, oriented, aspherical 3-manifold and give complete invariants for the stable classification in this case. This is joint work with Markus Land, Mark Powell and Peter Teichner.