The Exchange of Orientifold Two-Planes in M-theory

We propose an M-theory lift picture of the exchange among type IIA orientifold two-planes. This consists in wrapping a M5-brane on a three-cycle in the transverse space of the M-theory orientifold plane OM2. A flux quantization condition for the three-form self-dual field strength, on the worldvolume of the M5-brane is computed. This condition establishes the value which explains the relative charge between two different OM2-planes. Also, we find that the exchange of the four types of orientifold two-planes in string theory, has a common picture in M-theory. Moreover, we find that the assignment of the extra charge is fixed by cohomology and by the flux quantization of the field strength G in M-theory. We conclude that cohomology is sufficient to describe some orientifold properties in M-theory, that at string theory level, only K-theory is able to explain.