The authors present calculations of e⁺-H₂ scattering below the positronium formation threshold at 8.63 eV for the Sigma _g⁺, Sigma _u⁺, Pi _u and Pi _g symmetries using the generalized Kohn method. Mixing of the two lowest partial waves is allowed for in the Sigma _g⁺, Sigma _u⁺ and Pi _u symmetries, using a two channel K-matrix. Comparisons with Kohn calculations of the lowest partial waves of these symmetries show that mixing of partial waves has a relatively small effect on the contributions to the total scattering cross section at the energies considered. The Pi _g calculation includes only the lowest partial wave. As well as separable short-range correlation functions, the trial functions used in these calculations include Hylleraas-type functions containing the positron-electron distance as a linear factor and functions appropriate for taking into account long-range polarization of the hydrogen molecule.