The equivariant parametrized h-cobordism theorem, the non-manifold part

We construct a map from the suspension G-spectrum ?G?M of smooth compact G-manifold to equivariant A-theory spectrum AG(M), and we show that its fiber is, on fixed points, wedge stable h-cobordism spectra. This is constructed as spectral Mackey functors, which compatible with tom Dieck style splitting formulas points. In order reconcile different definitions functor, present new perspective viewing them multifunctors indexing categories for “rings many objects” modules over such. should be independent interest.