We give a classification of irreducible characters of finite groups of Lie type of p ′ p’ -degree, where p p is any prime different from the defining characteristic, in terms of local data. More precisely, we give a classification in terms of data related to the normalizer of a suitable Levi subgroup, which in many cases coincides with the normalizer of a Sylow p p -subgroup. The McKay conjecture asserts that there exists a bijection between characters of p ′ p’ -degree of a group and of the normalizer of a Sylow p p -subgroup. We hope that our result will constitute a major step towards a proof of this conjecture for groups of Lie type, and, in conjunction with a recent reduction result of Isaacs, Malle and Navarro, for arbitrary finite groups.