  We present a method where derivations of star-product algebras are used to
build covariant derivatives for noncommutative gauge theory. We write down a
noncommutative action by linking these derivations to a frame field induced by
a nonconstant metric. An example is given where the action reduces in the
classical limit to scalar electrodynamics on a curved background. We further
use the Seiberg-Witten map to extend the formalism to arbitrary gauge groups. A
proof of the existence of the Seiberg-Witten-map for an abelian gauge potential
is given for the formality star-product. We also give explicit formulas for the
Weyl ordered star-product and its Seiberg-Witten-maps up to second order.
