Torsion-freeness conjecture for algebraic cobordism of Rost motives

Let $G$ be a connected compact Lie group and let ${\mathbb G}$ be a $G_k$-torsor. Let $R({\mathbb G})$ be the associated Rost motive, let $\bar R({\mathbb G})$ denote its split form, and let $BP^*$ be the coefficient ring of Brown–Peterson theory. The restriction map is induced by passage from the torsor to its split form.

Algebraic cobordism torsion-freeness conjecture.

$$res_{\Omega}:\Omega^*(R({\mathbb G}))\to \Omega^*(\bar R({\mathbb G}))\subset BP^*\otimes P(y)$$

should be injective; equivalently, $\Omega^*(R({\mathbb G}))$ should be torsion free. This extends the injectivity verified in the paper for several spin groups and Rost motives. The statement is presented as a conjecture for connected compact Lie groups in general.