  The variant of Fedosov construction based on fairly general fiberwise product
in the Weyl bundle is studied. We analyze generalized star products of
functions, of sections of endomorphisms bundle, and those generating deformed
bimodule structure as introduced previously by Waldmann. Isomorphisms of
generalized Fedosov algebras are considered and their relevance for deriving
Seiberg-Witten map is described. The existence of the trace functional is
established. For star products and for the trace functional explicit
expressions, up to second power of deformation parameter, are given. The
example of symmetric part of noncommutativity tensor is discussed as a case
with possible field-theoretic application.
