  We prove that, for a K3 surface in characteristic p > 2, the automorphism
group acts on the nef cone with a rational polyhedral fundamental domain and on
the nodal classes with finitely many orbits. As a consequence, for any
non-negative integer g, there are only finitely many linear systems of
irreducible curves on the surface of arithmetic genus g, up to the action of
the automorphism group.
