  Context: The nature of type Ia supernovae (SNe Ia) is still unclear.
Metallicities may have an important effect on their properties.
  Aims: In this paper, we study the He star donor channel towards SNe Ia
comprehensively and systematically at various metallicities.
  Methods: Employing Eggleton's stellar evolution code with the optically thick
wind assumption, we calculated about 10 000 WD + He star systems and obtained
SN Ia production regions of the He star donor channel with metallicities
Z=0.03, 0.02, 0.004 and 0.0001. According to a detailed binary population
synthesis approach, we also obtained SN Ia birthrates at various metallicities.
  Results: Our study shows that both the initial mass of the He donor star and
the initial orbital period for SNe Ia increase with metallicity, while the
minimum initial mass of the carbon--oxygen white dwarfs producing SNe Ia
decreases with metallicity. For a constant star-formation galaxy, SN Ia
birthrates increase with metallicity. If a single starburst is assumed, SNe Ia
occur systemically earlier and the peak value of the birthrate is larger for a
high Z, and the He star donor channel with different metallicities can produce
the young SNe Ia with delay times $\sim$45-220Myr.
