  The open descendants of simple current automorphism invariants are
constructed. We consider the case where the order of the current is two or odd.
We prove that our solutions satisfy the completeness conditions, positivity and
integrality of the open and closed sectors and the Klein bottle constraint
(apart from an interesting exception). In order to do this, we derive some new
relations between the tensor Y and the fixed point conformal field theory. Some
non-standard Klein bottle projections are considered as well.
