We report vibrational excitation (νi =0→ νf =1) and total cross sections for positron scattering by H2. The Feshbach projection operator formalism was employed to vibrationally resolve the fixed-nuclei phase shifts obtained with the Schwinger multichannel method. The near-threshold behavior of the vibrational excitation cross section is in good agreement with available experimental data. Though our fixed-nuclei calculations do not indicate the existence of a e+ - H2 virtual state, a proper description of the T matrix threshold behavior is essential (the adiabatic approximation is inadequate). The projection operator approach has long been a powerful tool for studies of nuclear dynamics in electron-molecule collisions, and its application to positron scattering is timely since couplings to nuclear degrees of freedom are known to be very important at low impact energies. © 2007 The American Physical Society.765 Gilbert, S.J., Kurz, C., Greaves, R.G., Surko, C.M., (1997) Appl. Phys. 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