arXiv:1109.3867 Twisted Morava K-theory and E-theory from arXiv Front: math.AT by Hisham Sati, Craig Westerland For an integral cohomology class H of degree n+2 on a space X, we define twisted Morava K-theory K(n)(X; H) at the prime 2, as well as an integral analogue. We explore properties of this twisted cohomology theory, study a twisted Atiyah-Hirzebruch spectral sequence, and give a universal coefficient theorem (in the spirit of Khorami). We extend the construction to define twisted Morava E-theory, and provide applications to string theory and M-theory.
nLab page on Twisted Morava K-theory