Construction of numerically trivial automorphisms of Enriques surfaces in characteristic 2

Let S be an Enriques surface defined over an algebraically closed field in characteristic p.  An automorphism f is called numerically trivial if it acts identically on the second l-adic cohomology group of S. In case that  p = 0 of p>2, S. Mukai, Y. Namikawa, I. Dolgachev and G. Martin examined numerically trivial automorphisms of Enriques surfaces and showed that there exists no non-trivial numerically trivial automorphism of odd order for Enriques surfaces. In this talk, we will construct some examples of Enriques surfaces S with numerically trivial automorphisms of odd order >1 in characteristic 2.