Methodological gap: proving the Morava analogue without explicit computations

Develop a proof of Conjecture 1 (the Morava K-theory analogue of Yagita’s conjecture) that does not rely on prior explicit computation of the algebraic Morava K-theory K(n)*(G) as a module for the reductive group G = K_C.

Background

The authors prove Conjecture 1 for orthogonal and spinor groups using explicit computations of algebraic Morava K-theory, but they highlight the absence of a general method that avoids such calculations.

This remark pinpoints a specific methodological open question about finding a more conceptual or uniform approach to the conjecture.