Descente de Shintani et Restriction des Scalaires

An interpretation is given of the Shintani descent from thepoints of a connected algebraic group over a finite field toits group of points over a subfield in terms of a Shintani descentbetween two different rational structures over the same finitefield, using restriction of scalars. From this a generalizationis deduced of a result of Gyoja's on the Shintani descent ofDeligne–Lusztig characters of a finite group of Lie type.