Global May functor existence conjecture

Let $E$ be a Landweber exact spectrum, and let $\mathbf{MU}$ denote the global equivariant analogue of complex cobordism. A global version of May's functor would assign to $E$ the relative smash product $\mathbf{MU}\wedge_{MU}E$, and weak global Landweber exactness is the corresponding global exactness condition. Global May functor existence conjecture. There is a global version of May's functor $E\mapsto\mathbf{MU}\wedge_{MU}E$ which takes Landweber exact spectra to weakly globally Landweber exact spectra. This conjecture concerns the construction of a global refinement of May's equivariant construction and its preservation of Landweber exactness; the source gives no resolution.