  The generalized SU(2) Proca theory is a vector-tensor modified gravity theory
where the action is invariant under both diffeomorphisms and global internal
transformations of the SU(2) group. This work constitutes the first approach to
investigate the physical properties of the theory at astrophysical scales. We
have found solutions that naturally generalize the particle-like solutions of
the Einstein-Yang-Mills equations, also known as gauge boson stars. Under the
requirement that the solutions must be static, asymptotically flat, and
globally regular, the t'Hooft-Polyakov magnetic monopole configuration for the
vector field rises as one viable possibility. The solutions have been obtained
analytically through asymptotic expansions and numerically by solving the
boundary value problem. We have found new features in the solutions such as
regions with negative effective energy density and imaginary effective charge.
We have also obtained a new kind of globally charged solutions for some region
in the parameter space of the theory. Furthermore, we have constructed
equilibrium sequences and found turning points in some cases. These results
hint towards the existence of stable solutions which are absent in the
Einstein-Yang-Mills case.
