Subspace arrangements and motives of classifying stacks of reflection groups

We prove that the motivic class of the classifying stack of every finite linear (or projective) reflection group is trivial in the Grothendieck ring of algebraic stacks over any field containing a primitive root of unity of degree the exponent of the group. Our proof of these geometric statements rests on a combinatorial analysis of a formula by T. Ekedahl that we interpret in terms of certain subspace arrangements associated to any representation of a finite group. As a byproduct we obtain different geometric applications based on previous results of the second author.