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