  The category of rational O(2)-equivariant cohomology theories has an
algebraic model A(O(2)), as established by work of Greenlees. That is, there is
an equivalence of categories between the homotopy category of rational
O(2)-equivariant spectra and the derived category of the abelian model
DA(O(2)). In this paper we lift this equivalence of homotopy categories to the
level of Quillen equivalences of model categories. This Quillen equivalence is
also compatible with the Adams short exact sequence of the algebraic model.
