  The universal curve p:C->\Mbar over the moduli space \Mbar of stable r-spin
maps to a target K\"ahler manifold X carries a universal spinor bundle L->C.
Therefore the moduli space \Mbar itself carries a natural K-theory class Rp_*L.
  We introduce a twisted r-spin Gromov-Witten potential of X enriched with
Chern characters of Rp_*L. We show that the twisted potential can be
reconstructed from the ordinary r-spin Gromov-Witten potential of X via an
operator that assumes a particularly simple form in Givental's quantization
formalism.
