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The Υ(nS) production and polarization at high energies is studied in the framework of kT-factorization approach. Our consideration is based on the non-relativistic QCD formalism for bound states formation and off-shell production amplitudes for hard partonic subprocesses. The direct production mechanism and feed-down contributions from radiative χb(mP) decays are taken into account. The transverse momentum dependent gluon densities in a proton were derived from the Ciafaloni–Catani–Fiorani–Marchesini evolution equation and Kimber-Martin-Ryskin prescription. Treating the non-perturbative color octet transitions in terms of the mulitpole radiation theory, we extract the corresponding non-perturbative matrix elements for Υ(nS) and χb(mP) mesons from a combined fit to Υ(nS) transverse momenta distributions measured by the CMS and ATLAS Collaborations at the LHC energies √s=7 and 13 TeV and from the relative production rate R(χb(nP)/Υ(nS)) measured by the LHCb Collaboration at √s=7 and 8 TeV. Then we apply the extracted values to investigate the polarization parameters λθ, λφ and λθφ, which determine the Υ(nS) spin density matrix. Our predictions have a good agreement with the currently available data within the theoretical and experimental uncertainties.