A discrete model of O(2)-homotopy theory

A. Blumberg has shown that the category of triples consisting of a simplicial set, a cyclic set and appropriate compatibility data serves as a discrete model for the homotopy theory of spaces with an S1-action. We show that the category of triples consisting of a Δ(Z/2)-set, dihedral set and appropriate compatibility data serves as a model for the homotopy theory of O(2)-spaces.