The norm varieties and the varieties with special correspondences
play a major role in the proof of the Bloch-Kato Conjecture
by M.Rost and V.Voevodsky. In the present paper we show that a variety
which possesses a special correspondence is a norm variety.
As an unexpected application we give a positive answer
to a problem of J.-P.Serre about groups of type E8 over the field of
rational numbers. Apart from this we include the proof of the Voevodsky
conjecture about nu_n-varieties which is due to A.Vishik. This result plays
an important role in our proofs.