  We construct noncommutative gauge theories based on the notion of the Weyl
bundle, which appears in Fedosov's construction of deformation quantization on
an arbitrary symplectic manifold. These correspond to D-brane worldvolume
theories in non-constant B-field and curved backgrounds in string theory. All
such theories are embedded into a "universal" gauge theory of the Weyl bundle.
This shows that the combination of a background field and a noncommutative
field strength has universal meaning as a field strength of the Weyl bundle. We
also show that the gauge equivalence relation is a part of such a "universal"
gauge symmetry.
