The product formula in unitary deformation K-theory

For finitely generated groups G and H, we prove that there is a weak equivalence KG ∧ _ku KH ≃ K(G × H) of ku-algebra spectra, where K denotes the "unitary deformation K-theory" functor. Additionally, we give spectral sequences for computing the homotopy groups of KG and Hℤ ∧ _kuKG in terms of connective K-theory and homology of spaces of G-representations.