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In this paper we construct homogeneous star products of Weyl type on everycotangent bundle $T^*Q$ by means of the Fedosov procedure using a symplectictorsion-free connection on $T^*Q$ homogeneous of degree zero with respect tothe Liouville vector field. By a fibrewise equivalence transformation weconstruct a homogeneous Fedosov star product of standard ordered typeequivalent to the homogeneous Fedosov star product of Weyl type.Representations for both star product algebras by differential operators onfunctions on $Q$ are constructed leading in the case of the standard orderedproduct to the usual standard ordering prescription for smooth complex-valuedfunctions on $T^*Q$ polynomial in the momenta (where an arbitrary fixedtorsion-free connection $\nabla_0$ on $Q$ is used). Motivated by the flat case$T^* R^n$ another homogeneous star product of Weyl type corresponding to theWeyl ordering prescription is constructed. The example of the cotangent bundleof an arbitrary Lie group is explicitly computed and the star product given byGutt is rederived in our approach.Comment: 31 pages, LaTeX2e, no picture

Homogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation