Morava J-invariant - Nikita Geldhauser; Andrei Lavrenov; Victor Petrov; Pavel Sechin (Forum of Mathematics, Sigma, 2025)
We compute the co-multiplication of the algebraic Morava K-theory for split orthogonal groups. This allows us to compute the decomposition of the Morava motives of generic maximal orthogonal Grassmannians and to compute a Morava K-theory analogue of the J-invariant in terms of the ordinary (Chow) J-invariant.