  Recently a construction was given for the stress tensors of all sectors of
the general current-algebraic orbifold A(H)/H, where A(H) is any
current-algebraic conformal field theory with a finite symmetry group H. Here
we extend and further analyze this construction to obtain the mode formulation
of each sector of each orbifold A(H)/H, including the twisted current algebra,
the Virasoro generators, the orbifold adjoint operation and the commutator of
the Virasoro generators with the modes of the twisted currents. As
applications, general expressions are obtained for the twisted current-current
correlator and ground state conformal weight of each twisted sector of any
permutation orbifold A(H)/H, H \subset S_N. Systematics are also outlined for
the orbifolds A(Lie h(H))/H of the (H and Lie h)-invariant conformal field
theories, which include the general WZW orbifold and the general coset
orbifold. Finally, two new large examples are worked out in further detail: the
general S_N permutation orbifold A(S_N)/S_N and the general inner-automorphic
orbifold A(H(d))/H(d).
