  We present a detailed analysis of the collider signatures of TeV-scale
massive vector bosons motivated by the hints of lepton flavour non-universality
observed in $B$-meson decays. We analyse three representations that necessarily
appear together in a large class of ultraviolet-complete models: a
colour-singlet ($Z'$), a colour-triplet (the $U_1$ leptoquark), and a colour
octet ($G'$). Under general assumptions for the interactions of these exotic
states with Standard Model fields, including in particular possible
right-handed and flavour off-diagonal couplings for the $U_1$, we derive a
series of stringent bounds on masses and couplings that constrain a wide range
of explicit new-physics models.
