In this paper we first give condtions esuring unicity for the Jordan decomposition of irreducible characters of finite groups of Lie type with a connected center. In the case of groups with a non-connected centre, we extend Lusztig's parametrization of irreductible characters. This generalization is such that formulas giving the multiplicities of irreducible characters in Deligne-Lusztig characters are the natural generalizations of the connected center case (i.e., given by “Fourier transforms”). We then compute under suitable assumptions (which we prove to be verified in the case of principal series characters) Shintani descent of irreducible characters using this parametrization and the Fourier transform.