Descent equalities and the inductive McKay condition for types [formula omitted] and [formula omitted

Abstract

We establish the inductive McKay condition introduced by Isaacs-Malle-Navarro [14] for finite simple groups of Lie types Bl (l≥2), E6, E62 and E7, thus leaving open only the types D and D2. We bring to the methods previously used by the authors for type C[8] some descent arguments using Shintani's norm map. This provides for types different from A,D,D2 a uniform proof of the so-called global requirement of the criterion given by the second author in [32, 2.12]. The local requirements from that criterion are verified through a detailed study of the normalizers of relevant Levi subgroups and their characters.