  We investigate the existence of the skyrmion field in the background of an
asymptotically flat stationary reflecting star.
  For this purpose, we consider the Einstein Skyrme system for which there is a
skyrmion hair in the black hole case. We discuss spherically symmetric
skyrmions and employ the hedgehog ansatz for the skyrmion field. We show that,
in contrast to the black hole there is no skyrmion hair for a reflecting star.
