D-branes and orientifolds of SO(3)

We study branes and orientifolds on the group manifold of SO(3). We consider particularly the case of the equatorial branes, which are projective planes. We show that a Dirac-Born-Infeld action can be defined on them, although they are not orientable. We find that there are two orientifold projections with the same spacetime action, which differ by their action on equatorial branes.