  For any odd characteristic p=2 mod 3, we exhibit an explicit automorphism on
the supersingular K3 surface of Artin invariant one which does not lift to any
characteristic zero model. Our construction builds on elliptic fibrations to
produce a closed formula for the automorphism's characteristic polynomial on
second cohomology, which turns out to be an irreducible Salem polynomial of
degree 22 with coefficients varying with p.
