  Fulton defined classes in the Chow group of a quasi-projective scheme $M$
which reduce to its Chern classes when $M$ is smooth. When $M$ has a perfect
obstruction theory, Siebert gave a formula for its virtual cycle in terms of
its total Fulton class.
  We describe K-theory classes on $M$ which reduce to the exterior algebra of
differential forms when $M$ is smooth. When $M$ has a perfect obstruction
theory, we give a formula for its K-theoretic virtual structure sheaf in terms
of these classes.
