NNLO contributions to inclusive-jet production in DIS and determination of \alpha_s

We present the first calculation of inclusive jet production in deep-inelastic scattering with approximate next-to-next-to-leading order (aNNLO) contributions, obtained from a unified threshold resummation formalism. The leading coefficients are computed analytically. We show that the aNNLO contributions reduce the theoretical prediction for jet production in deep-inelastic scattering, improve the description of the final HERA data in particular at high photon virtuality Q^2 and increase the central fit value of the strong coupling constant.