  In tensor products of a left-right symmetric CFT, one can define permutation
orientifolds by combining orientation reversal with involutive permutation
symmetries. We construct the corresponding crosscap states in general rational
CFTs and their orbifolds, and study in detail those in products of affine
U(1)_2 models or N=2 minimal models. The results are used to construct
permutation orientifolds of Gepner models. We list the permutation orientifolds
in a few simple Gepner models, and study some of their physical properties -
supersymmetry, tension and RR charges. We also study the action of
corresponding parity on D-branes, and determine the gauge group on a stack of
parity-invariant D-branes. Tadpole cancellation condition and some of its
solutions are also presented.
