[en] We develop an operator formulation for the Drell-Yan production of lepton pair in hadron-hadron collisions. We employ the generalized Wilson operator expansion where the main ingredients are the Keldysh formalism and the gauge-invariant nonlocal operators. Compared to conventional approaches based on the collinear expansion of the relevant diagrams, our approach has an advantage of preserving explicitly Lorentz and gauge invariance, and thus provides a convenient framework for systematic treatment of the Drell-Yan processes. Utilizing the background field method, we derive the coefficient functions at tree level in the generalized operator expansion, which are relevant to the asymmetry observables through order 1/Q (twist-3) for the case with polarized beams. We emphasize novel role played by the 'color octet terms', which are generated by the Fierz rearrangement of the quark fields in the electromagnetic currents. We demonstrate that at higher twist the quark-antiquark color octet terms produce 'color singlet terms' due to quark-antiquark-gluon correlation. (author)