 Now suppose that "G" is a reductive group over some field "k" with separable closure "K".Over "K", "G" has a root datum, and this comes with an action of the Galois group "Gal"("K"/"k").The identity component L"G"o of the "L"-group is the connected complex reductive group of the dual root datum; this has an induced action of the Galois group "Gal"("K"/"k").