  We consider properties of solitons in general orbifolds in the algebraic
quantum field theory framework and constructions of solitons in affine and
permutation orbifolds. Under general conditions we show that our construction
gives all the twisted representations of the fixed point subnet. This allows us
to prove a number of conjectures: in the affine orbifold case we clarify the
issue of ``fixed point resolutions''; in the permutation orbifold case we
determine all irreducible representations of the orbifold, and we also
determine the fusion rules in a nontrivial case, which imply an integral
property of chiral data for any completely rational conformal net.
