The Morava K-theory analogue of Yagita's conjecture

Let $K$ be a compact connected Lie group, $T$ its maximal torus, and $\pi\colon K\rightarrow K/T$ the natural projection. Denote by $G=K_{\mathbb C}$ the corresponding split reductive group over $\mathbb C$. For $A=\mathrm K(n)$ or $A=\mathrm{CK}(n)$, consider the algebraic theory $A^*(G)$ and the topological theory $A^*_{\mathrm{top}}(K/T)$. The Morava K-theory analogue of Yagita's conjecture. One has

$$A^*(G)\cong\pi^*\big(A^*_{\mathrm{top}}(K/T)\big).$$

This is presented as the analogue, for Morava K-theory and connective Morava K-theory, of Yagita's conjectural comparison between algebraic and topological cobordism. The supplied text does not state whether this claim is proved or remains open.