  Near-solar metallicity (and low-redshift) Pair-Instability Supernova (PISN)
candidates challenge stellar evolution models. Indeed, at such a metallicity,
even an initially very massive star generally loses so much mass by stellar
winds that it will avoid the electron-positron pair-creation instability. We
use recent results showing that a magnetic field at the surface of a massive
star can significantly reduce its effective mass-loss rate to compute magnetic
models of very massive stars (VMSs) at solar metallicity and explore the
possibility that such stars end as PISNe. We implement the quenching of the
mass loss produced by a surface dipolar magnetic field into the Geneva stellar
evolution code and compute new stellar models with an initial mass of
$200\,M_\odot$ at solar metallicity, with and without rotation. It considerably
reduces the total amount of mass lost by the star during its life. For the
non-rotating model, the total (CO-core) mass of the models is $72.8\,M_\odot$
($70.1\,M_\odot$) at the onset of the electron-positron pair-creation
instability. For the rotating model, we obtain $65.6\,M_\odot$
($62.4\,M\odot$). In both cases, a significant fraction of the internal mass
lies in the region where pair instability occurs in the $\log(T)-\log(\rho)$
plane. The interaction of the reduced mass loss with the magnetic field
efficiently brakes the surface of the rotating model, producing a strong shear
and hence a very efficient mixing that makes the star evolve nearly
homogeneously. The core characteristics of our models indicate that solar
metallicity models of magnetic VMSs may evolve to PISNe (and pulsation PISNe).
