  We introduce a Grothendieck ring of higher Artin stacks generalizing the
Grothendieck ring of algebraic varieties. We show that this ring is not trivial
by noticing that it factors the invariant "number of rational points over a
finite field". We also introduce the notion of "special Artin stacks", which by
definition have affine homotopy groups \pi_{i}, and furthermore unipotent for
i>1. Our principal theorem states that the natural inclusion morphism from the
Grothendieck ring of varieties to the Grothendieck ring of special Artin stacks
is an isomorphism after inverting the class of the affine line L and the
classes of L^{i}-1 for all i>0. We deduce from this that several numerical
invariants defined for varieties (e.g. Hodge numbers, l-adic Euler
characteristic ...) extend uniquely to invariants defined for special Artin
stacks. In particular we obtain a trace formula for special Artin stacks of
finite type over a finite field, identifying the number of rational points as
the trace of the Frobenius acting on the l-adic Euler characteristic.
