Universality conjecture for the formal group of geometric cobordisms over Hopf algebras

Let $H$ be a (topological) Hopf algebra and let ${\frak F}(x\otimes 1,1\otimes x)$ denote the formal group constructed from geometric cobordisms over $H$.

Universality conjecture. The formal group ${\frak F}(x\otimes 1,1\otimes x)$ is the universal object in the category of formal groups over a (topological) Hopf algebra.

This asserts that the formal group of geometric cobordisms has the expected universal property in the category of formal groups over topological Hopf algebras. The surrounding text recalls that the ordinary formal group of geometric cobordisms is known to be universal, but does not provide a resolution of this Hopf-algebraic formulation.