  We give a full description of the Chow ring of the complex Cayley plane, the
simplest of the exceptional flag varieties. We describe explicitely the most
interesting of its Schubert varieties and compute their intersection products.
Translating our results in the Borel presentation, i.e. in terms of Weyl group
invariants, we are able to compute the degree of the variety of reductions
$Y_8$ introduced in our related preprint math.AG/0306328.
