  We consider the classification of BPS and non-BPS D-branes in orientifold
models. In particular we construct all stable BPS and non-BPS D-branes in the
Gimon-Polchinski (GP) and Dabholkar-Park-Blum-Zaffaroni (DPBZ) orientifolds and
determine their stability regions in moduli space as well as decay products. We
find several kinds of integrally and torsion charged non-BPS D-branes. Certain
of these are found to have projective representations of the orientifold
$\times$ GSO group on the Chan-Paton factors. It is found that the GP
orientifold is not described by equivariant orthogonal K-theory as may have
been at first expected. Instead a twisted version of this K-theory is expected
to be relevant.
