J.P.C.Greenlees ``Rational O(2)-equivariant cohomology theories.'' 8
pp

A complete algebraic model is given for rational O(2)-spectra. The main 
input is the model for SO(2)-spectra described in ``Rational 
S1-equivariant stable homotopy theory'', and the special case of 
``Rational Mackey functors for compact Lie groups I'' applying to O(2). 
It turns out that any O(2)-spectrum is described by an SO(2)-spectrum 
with O(2)/SO(2)-action, together with an equivariant sheaf over the space 
of dihedral subgroups of O(2).