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Using the construction of Colliot-Th\'el\`ene and Ojanguren, we exhibit anexample of a smooth projective geometrically rational variety X defined over afinite field F_p with an algebraic closure \bar F_p and the absolute Galoisgroup G, such that the group H^3_nr(X, Z/2) is nonzero and the map CH^2(X)\toCH^2(\bar X)^G is not surjective.

Sur le groupe de Chow de codimension deux des vari\'et\'es sur les corps finis