  Quantum fluctuations of a complex, baryonic charged scalar field caused by
inflation can generate large domains, which convert later into antimatter
regions. As a result the Universe can become globally matter-dominated, with
minor contribution of antimatter regions. The distribution and evolution of
such antimatter regions could cause every galaxy to be a harbour of an
anti-star globular cluster. At the same time, the scenario does not lead to
large-scale isocuvature perturbations, which would disturb observable CMB
anisotropy. The existence of one of such antistar globular cluster in our
Galaxy does not contradict the observed $\gamma$-ray background, but the
expected fluxes of $\bar{\rm ^4He}$ and $\bar{\rm ^3He}$ from such an
antimatter object are definitely accessible to the sensitivity of the coming
AMS--02 experiment.
