  The standard Klein bottle coefficient in the construction of open descendants
is shown to equal the Frobenius-Schur indicator of a conformal field theory.
Other consistent Klein bottle projections are shown to correspond to simple
currents. These observations enable us to generalize the standard open string
construction from C-diagonal parent theories to include non-standard Klein
bottles. Using (generalizations of) the Frobenius-Schur indicator we prove
positivity and integrality of the resulting open and closed string state
multiplicities for standard as well as non-standard Klein bottles.
