  This paper concerns a class of orbital integrals in Lie algebras over p-adic
fields. The values of these orbital integrals at the unit element in the Hecke
algebra count points on varieties over finite fields. The construction, which
is based on motivic integration, works both in characteristic zero and in
positive characteristic. As an application, the Fundamental Lemma for this
class of integrals is lifted from positive characteristic to characteristic
zero. The results are based on a formula for orbital integrals as distributions
inflated from orbits in the quotient spaces of the Moy-Prasad filtrations of
the Lie algebra. This formula is established by Fourier analysis on these
quotient spaces.
