  Free string theory on the plane-wave background displays a discrete Z2
symmetry exchanging the two transverse SO(4) rotation groups. This symmetry
should be respected also at the interacting level. We show that the zero mode
structure proposed in hep-th/0208148 can be completed to a full kinematical
vertex, contrary to claims appeared in the previous literature. We also comment
on the relation with recent works on the string-bit formalism and on the
comparison with the field theory side of the correspondence.
