  Open descendants with boundaries and crosscaps of non-trivial automorphism
type are studied. We focus on the case where the bulk symmetry is broken to a
Z_2 orbifold subalgebra. By requiring positivity and integrality for the open
sector, we derive a unique crosscap of automorphism type g \in Z_2 and a
corresponding g-twisted Klein bottle for a charge conjugation invariant. As a
specific example, we use T-duality to construct the descendants of the true
diagonal invariant with symmetry preserving crosscaps and boundaries.
