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 explo red, and are interpreted as arising from brane intersections with planes. W e find new variants of the O0 and of an orbifold line (OF1) and determine t heir tensions in some cases. A systematic review of orientifolds, M orienti folds, and known M-lifts, with some new clarifications is included together with a discussion of the role of T-duality.