Twisted Morava K–theory and connective covers of Lie groups

Twisted Morava K-theory, along with computational techniques, including a universal coefficient theorem and an Atiyah-Hirzebruch spectral sequence, was introduced by Craig Westerland the first author. We employ these techniques to compute twisted K-theory of all connective covers stable orthogonal group unitary group, their classifying spaces, as well spheres Eilenberg-MacLane spaces. This extends case some results Ravenel Wilson Kitchloo, Laures, for K-theory. also generalizes chromatic levels computations Khorami (and in part those Douglas) at level one, i.e. establish that natural twists cases, there are only two possibilities: either homology vanishes, or it is isomorphic untwisted homology. provide variant on twist mod 2 cohomology place integral cohomology.