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We present the first fully differential next-to-leading order QCD calculationfor lepton production in transversely polarized hadronic collisions, pp -> l X, where the lepton arises from the decay of an electroweak gauge boson. Thecalculation is implemented in the Monte-Carlo like code `CHE' that alreadyincludes the unpolarized and longitudinally polarized cross sections and may bereadily used to perform a comparison to experimental data and to extractinformation on the related parton distributions. We analyze the perturbativestability of the cross-section and double spin asymmetry A_TT at RHICkinematics. We find that the QCD corrections are non-negligible even at thelevel of asymmetries and that they strongly depend on the lepton kinematics.Furthermore, we present two scenarios for transversely polarized partondistributions, based on the de Florian-Sassot-Stratmann-Vogelsang (DSSV) set oflongitudinally parton densities and fully evolved to NLO accuracy, that can beused for the evaluation of different observables involving transversepolarization.

Transversely polarized Drell-Yan asymmetry A_TT at NLO