  The twisted boundary conditions and associated partition functions of the
conformal sl(2) A-D-E models are studied on the Klein bottle and the M\"obius
strip. The A-D-E minimal lattice models give realization to the complete
classification of the open descendants of the sl(2) minimal theories. We
construct the transfer matrices of these lattice models that are consistent
with non-orientable geometries. In particular, we show that in order to realize
all the Klein bottle amplitudes of different crosscap states, not only the
topological flip on the lattice but also the involution in the spin
configuration space must be taken into account. This involution is the $Z_2$
symmetry of the Dynkin diagrams which corresponds to the simple current of the
Ocneanu algebra.
