  A. Ocneanu has observed that a mysterious orbifold phenomenon occurs in the
system of the M_infinity-M_infinity bimodules of the asymptotic inclusion, a
subfactor analogue of the quantum double, of the Jones subfactor of type
A_2n+1. We show that this is a general phenomenon and identify some of his
orbifolds with the ones in our sense as subfactors given as simultaneous fixed
point algebras by working on the Hecke algebra subfactors of type A of Wenzl.
That is, we work on their asymptotic inclusions and show that the
M_infinity-M_infinity bimodules are described by certain orbifolds (with
ghosts) for SU(3)_3k. We actually compute several examples of the (dual)
principal graphs of the asymptotic inclusions. As a corollary of the
identification of Ocneanu's orbifolds with ours, we show that a non-degenerate
braiding exists on the even vertices of D_2n, n>2.
