Hopkins's Wilson space hypothesis for algebraic cobordism

Let $k$ be a field, let $\bMGL$ denote the motivic algebraic cobordism spectrum, let $\bT$ be the motivic suspension coordinate, and let $\bDM(k)$ be the category of motives over $k$. For each $n\in\mathbb{Z}$, write $\Omega^{\infty-n}_{\bT}\bMGL$ for the corresponding motivic infinite loop space and $M(\Omega^{\infty-n}_{\bT}\bMGL)$ for its motive in $\bDM(k)$. Hopkins's Wilson space hypothesis. For every $n\in\mathbb{Z}$, the motive $M(\Omega^{\infty-n}_{\bT}\bMGL)\in\bDM(k)$ is pure Tate. This hypothesis predicts that all motivic infinite loop spaces of algebraic cobordism have motives built from Tate motives; the source gives no resolution, so the assertion remains open.