High-spin states and signature inversion in odd-odd Lu168

High-spin states of the odd-odd nucleus $^{168}\mathrm{Lu}$ were populated in the $^{123}\mathrm{Sb}(^{48}\mathrm{Ca},3\mathrm{n})^{168}\mathrm{Lu}$ reaction at a beam energy of 203 MeV and decay $\ensuremath{\gamma}$ rays measured using the Gammasphere spectrometer array. The level scheme has been extended from spin 27 to 50 $\ensuremath{\hbar}$, and three new rotational bands have been added. A number of interband linking transitions were revealed, so that all but two bands could be connected with each other. High-spin band crossings, above the first $\ensuremath{\nu}{i}_{13/2}$ alignment, are delineated in most bands. Significant signature inversions are identified for the first time in the bands involving both favored and unfavored signatures of the $\ensuremath{\pi}{h}_{9/2}$ orbital, which are likely caused by a residual proton-neutron interaction. A signature inversion with small amplitude is also observed in the $\ensuremath{\pi}{d}_{5/2}\ensuremath{\bigotimes}\ensuremath{\nu}{i}_{13/2}$ band. Configurations are suggested for all bands based on their experimental properties, with the help of Cranked Shell Model calculations. No evidence is found for triaxial strongly deformed structures that were predicted by the calculations.