We establish the inductive McKay condition introduced by Isaacs-Malle-Navarro [IMN07] for finite simple groups of Lie types B l (l ≥ 2), E 6 , 2 E 6 and E 7 , thus leaving open only the types D and 2 D. We bring to the methods previously used by the authors for type C [CS17b] some descent arguments using Shintani's norm map. This provides for types different from A, D, 2 D a uniform proof of the so-called global requirement of the criterion given by the second author in [S12, 2.12]. The local requirements from that criterion are verified through a detailed study of the normalizers of relevant Levi subgroups and their characters.