Sur les caract\`eres des groupes r\'eductifs finis : applications aux groupes sp\'eciaux lin\'eaires et unitaires

In the first chapters, this paper contains a survey on the theory of ordinary characters of finite reductive groups with non-connected centre. The last chapters are devoted to the proof of Lusztig's conjecture on characteristic functions of character sheaves for all finite reductive groups of type A, split or not.