  We characterize the irreducible polynomials that occur as a characteristic
polynomial of an automorphism of an even unimodular lattice of given signature,
generalizing a theorem of Gross and McMullen. As part of the proof, we give a
general criterion in terms of Witt groups for a bilinear form equipped with an
action of a group G over a discretely valued field to contain a unimodular
G-stable lattice.
