Higher torsion in the Morava \(K\)-theory of \(SO(m)\) and \(Spin(m)\) (Q5939223)

This paper is a continuation of [\textit{J. Hunton}, \textit{M. Mimura}, \textit{T. Nishimoto} and \textit{B. Schuster}, ibid. 50, No. 4, 801-818 (1998; Zbl 0923.55004)]. The author determines the \(K(n)^*\)-module structure of the Morava \(K\)-theories \(K(n)^*(\text{SO}(m))\) and \(K(n)^* (\text{Spin}(m))\), for the special orthogonal groups and the spinor groups, at the prime 2. The main tool is the Atiyah-Hirzebruch spectral sequence.