We present a dense model grid with tailored input chemical composition appropriate for the Large Magellanic Cloud. We use a one-dimensional hydrodynamic stellar evolution code, which accounts for rotation, transport of angular momentum by magnetic fields, and stellar wind mass loss to compute our detailed models. We calculate stellar evolution models with initial masses of 70-500 Msun and with initial surface rotational velocities of 0-550 km/s, covering the core-hydrogen burning phase of evolution. We find our rapid rotators to be strongly influenced by rotationally induced mixing of helium, with quasi-chemically homogeneous evolution occurring for the fastest rotating models. Above 160 Msun, homogeneous evolution is also established through mass loss, producing pure helium stars at core hydrogen exhaustion independent of the initial rotation rate. Surface nitrogen enrichment is also found for slower rotators, even for stars that lose only a small fraction of their initial mass. For models above 150 MZAMS, and for models in the whole considered mass range later on, we find a considerable envelope inflation due to the proximity of these models to their Eddington limit. This leads to a maximum zero-age main sequence surface temperature of 56000 K, at 180 Msun, and to an evolution of stars in the mass range 50-100 Msun to the regime of luminous blue variables in the HR diagram with high internal Eddington factors. Inflation also leads to decreasing surface temperatures during the chemically homogeneous evolution of stars above 180 Msun. The cool surface temperatures due to the envelope inflation in our models lead to an enhanced mass loss, which prevents stars at LMC metallicity from evolving into pair-instability supernovae. The corresponding spin-down will also prevent very massive LMC stars to produce long-duration gamma-ray bursts, which might, however, originate from lower masses.
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