  We establish a formula for the classes of certain tori in the Grothendieck
ring of varieties, in terms of its lambda-structure. More explicitly, we will
see that if L* is the torus of invertible elements in the n-dimensional
separable k-algebra L, then the class of L* can be expressed as an alternating
sum of the images of the spectrum of L under the lambda-operations, multiplied
by powers of the Lefschetz class. This formula is suggested from the cohomology
of the torus, illustrating a heuristic method that can be used in other
situations. To prove the formula will require some rather explicit calculations
in the Grothendieck ring. To be able to make these we introduce a homomorphism
from the Burnside ring of the absolute Galois group of k, to the Grothendieck
ring of varieties over k. In the process we obtain some information about the
structure of the subring generated by zero-dimensional varieties.
