  We develop an integral version of Deligne cohomology for smooth proper real
varieties. For this purpose the role played by singular cohomology in the
complex case has to be replaced by ordinary bigraded G-equivariant cohomology,
where G=Gal(C/R). This is the G-equivariant counterpart of singular cohomology.
We establish the basic properties of the theory and give a geometric
interpretation for the groups in dimension 2 in weights 1 and 2.
