A measurement of inclusive jet cross sections in high-Q² neutral current deep-inelastic scattering is performed using data collected by the ZEUS detector at the HERA ep collider. The data were taken in the years 2004 to 2007 at a centre-of-mass energy of 318 GeV and correspond to an integrated luminosity of 347 pb⁻¹. Jets are reconstructed using the k⟂-algorithm in the Breit reference frame. They are measured as a function of the squared four-momentum transfer Q² and the transverse momentum of the jets in the Breit frame p⟂. The measurement is performed in the kinematic region of 150 GeV² < Q² < 15000 GeV² and 0.2 < y < 0.7, with y being the inelasticity. Jets are required to fulfil the conditions 7 GeV < p⟂ < 50 GeV and -1 < η < 2.5, where η is the pseudorapidity in the laboratory frame.
The measured jet cross sections are compared to previous measurements and perturbative QCD predictions. The measurement is used in a next-to-next-to-leading-order QCD analysis to simultaneously determine the parton distribution functions of the proton and the strong coupling constant. A significant improvement in accuracy is observed compared to similar determinations. The physical scale dependence of the strong coupling is investigated.