Un Groupe Hyperbolique Est Determine Par Son Bord

We construct on the boundary of a hyperbolic group (in Gromov'ssense) a natural visual measure and a natural crossratio. Weprove that the I-quasiconformal homeomorphisms (in Pansu's sense)between the boundaries of hyperbolic groups are the quasimöbiusmaps (that is, the bijections that almost preserve the crossratios),and that they are the extensions of the quasi-isometries betweenthe groups. We define a barycentre for every probability measureon the boundary without atom, extending the Douady-Earle construction.