  We compute the Chow-Witt rings of split quadrics over a field of
characteristic not two. We even determine the full bigraded I-cohomology and
Milnor-Witt cohomology rings, including twists by line bundles. The results on
I-cohomology corroborate the general philosophy that I-cohomology is an
algebro-geometric version of singular cohomology of real varieties: our
explicit calculations confirm that the I-cohomology ring of a split quadric
over the reals is isomorphic to the singular cohomology ring of the space of
its real points.
