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Bott periodicity plays an important role in topological K-theory. The purposeof this paper is to extend the periodicity theorem in a discrete context, whereall classical groups are involved and not just the general linear group. Thepresent paper generalizes previous results of the author [K1] and [K2], where 2was assumed to be invertible in the rings involved. For the proof, twoimportant ideas have to be mentioned : the first one is due to Ranicki [R] whointroduced a kind of "enlarged" orthogonal group ; the second one is a genuinecup-product between quadratic forms due to Clauwens [C]. As an example ofresults obtained, we prove that the higher Witt groups of a finite field ofcharacteristic 2 are all isomorphic to Z/2. They generalize in some sense theDickson and Arf invariants.

Le theoreme de periodicite en K-theorie hermitienne