A new invariant of Poisson manifolds, a Poisson K-ring, is
introduced. Evidence is given that this invariant is more tractable
than such invariants as Poisson (co)homology. A version of this
invariant is also defined for arbitrary Lie algebroids. Basic
properties of the Poisson K-ring areproved and the
Poisson K-rings are calculated for a number of examples.
In particular, for the zero Poisson structure the K-ring
is the ordinary K0-ring of the manifold and
for the dual space to a Lie algebra the K-ring is the
ring of virtual representations of the Lie algebra.
It is also shown that the K-ring is an invariant of
Morita equivalence. Moreover, the K-ring is a functor
on a category, the weak morita category, which generalizes
the notion of Morita equivalence of Poisson Manifolds.