  It is shown that the K3 spectra which refine the local rings of the moduli
stack of ordinary p-primitively polarized K3 surfaces in characteristic p allow
for an Eoo structure which is unique up to equivalence. This uses the Eoo
obstruction theory of Goerss and Hopkins and the description of the deformation
theory of such K3 surfaces in terms of their Hodge F-crystals due to Deligne
and Illusie. Furthermore, all automorphism of such K3 surfaces can be realized
by Eoo maps which are unique up to homotopy, and this can by rigidified to an
action if the automorphism group is tame.
