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The first results on K∗(892)± resonance production in inelastic pp collisions at LHC energies of √s = 5.02, 8, and 13 TeV are presented. The K∗(892)± has been reconstructed via its hadronic decay channel K∗(892)± → K0 S + π± with the ALICE detector. Measurements of transverse momentum distributions, pT-integrated yields, and mean transverse momenta for charged K∗(892) are found to be consistent with previous ALICE measurements for neutral K∗(892) within uncertainties. For pT > 1 GeV/c the K∗(892)± transverse momentum spectra become harder with increasing centre-of-mass energy from 5.02 to 13 TeV, similar to what previously observed for charged kaons and pions. For pT < 1 GeV/c the K∗(892)± yield does not evolve significantly and the abundance of K∗(892)± relative to K is rather independent of the collision energy. The transverse momentum spectra, measured for K∗(892)± at midrapidity in the interval 0 < pT < 15 GeV/c, are not well described by predictions of different versions of PYTHIA 6, PYTHIA 8 and EPOS-LHC event generators. These generators reproduce the measured pTintegrated K∗±/K ratios and describe well the momentum dependence for pT < 2 GeV/c.