  Let X be the wonderful compactification of a connected adjoint semisimple
group G defined over a number field K. We prove Manin's conjecture on the
asymptotic (as T\to \infty) of the number of K-rational points of X of height
less than T, and give an explicit construction of a measure on X(A),
generalizing Peyre's measure, which describes the asymptotic distribution of
the rational points G(K) on X(A). Our approach is based on the mixing property
of L^2(G(K)\G(A)) which we obtain with a rate of convergence.
