On the Serre conjecture for Artin characters in the geometric case

Let G be a finite group and A be a regular local ring on which G acts. Under certain assumptions on A and the action, Serre defined a function aG G which can be viewed as a higher dimensional analogue of Artin character, and conjectured that it is associated to a Q_-rational representation of G for any prime invertible in A. We prove this conjecture in the equal characteristic case.