On the algebraizability of formal deformations in K-cohomology

We show that algebraizability of the functors R¹π_*KM2,X and R²π_*KM2,X is a stable birational invariant for smooth and proper varieties π:X→ k defined over an algebraic extension k of Q. The same is true for the \'etale sheafifications of these functors as well. To get these results we introduce a notion of relative K-homology for schemes of finite type over a finite dimensional, Noetherian, excellent base scheme over a field. We include this material in an appendix.