  In math.QA/0311303 B. Feigin, G. Felder, and B. Shoikhet proposed an explicit
formula for the trace density map from the quantum algebra of functions on an
arbitrary symplectic manifold M to the top degree cohomology of M. They also
evaluated this map on the trivial element of K-theory of the algebra of quantum
functions. In our paper we evaluate the map on an arbitrary element of
K-theory, and show that the result is expressed in terms of the A-genus of M,
the Deligne-Fedosov class of the quantum algebra, and the Chern character of
the principal symbol of the element. For a smooth (real) symplectic manifold
(without a boundary), this result implies the Fedosov-Nest-Tsygan algebraic
index theorem.
