On orientifolds, discrete torsion, branes and M-theory

We find some lifts to M-theory of orientifold and orbifold planes including the O1, O3 and O5 planes of type IIB and their transformations under SL(2,ℤ). The possible discrete torsion variants (or K-theory classes) are explored, and are interpreted as arising from brane intersections with planes. We find new variants of the O0 and of an orbifold line (OF1) and determine their tensions in some cases. A systematic review of orientifolds, M orientifolds, and known M-lifts, with some new clarifications is included together with a discussion of the role of T-duality.