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. 
C\'edric Bonnaf\'e (LM-Besan\c{c}on)