Greenlees's universality conjecture for equivariant complex cobordism

Let $G$ be a finite abelian group, let $E$ be a complex oriented $G$-equivariant spectrum, and let $MU_G$ denote the canonical $G$-equivariant complex cobordism spectrum. The associated equivariant formal group laws have the structures of a complete algebra with comultiplication, an augmentation compatible with comultiplication, and elements indexed by the characters of $G$ as described above.

Greenlees's conjecture. There is a unique homomorphism of rings

$$\theta: MU_G^* \longrightarrow E^*$$

such that $\theta$ induces maps sending structures $(1)$, $(2)$, and $(3)$ for the canonical equivariant formal group law corresponding to $MU_G$ to the corresponding structures for $E$.

This asserts that equivariant complex cobordism is universal among complex oriented $G$-equivariant cohomology theories through its canonical equivariant formal group law. The supplied source does not state a resolution, so the conjecture is recorded as open.