  The construction of CP-invariant lattice chiral gauge theories and the
construction of lattice Majorana fermions with chiral Yukawa couplings is
subject to topological obstructions. In the present work we suggest lattice
extensions of charge and parity transformation for Weyl fermions. This enables
us to construct lattice chiral gauge theories that are CP invariant. For the
construction of Majorana-Yukawa couplings, we discuss two models with
symplectic Majorana fermions: a model with two symplectic doublets, and one
with an auxiliary doublet.
