Let X be a normal projective variety over an algebraically closed field and with numerically trivial canonical bundle, for instance a Calabi-Yau manifold. The Morrison – Kawamata cone conjecture predicts that the automorphism group of X acts with a rational polyhedral fundamental domain on the effective nef cone of X. We give a new proof of the Morrison–Kawamata cone conjecture for Enriques surfaces independent of their characteristic. It is based on the analysis of certain generically finite morphisms of degree two. This is joint work with Gebhard Martin and Tobias Schnieders.