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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 Iacomprehensively and systematically at various metallicities.  Methods: Employing Eggleton's stellar evolution code with the optically thickwind assumption, we calculated about 10 000 WD + He star systems and obtainedSN Ia production regions of the He star donor channel with metallicitiesZ=0.03, 0.02, 0.004 and 0.0001. According to a detailed binary populationsynthesis approach, we also obtained SN Ia birthrates at various metallicities.  Results: Our study shows that both the initial mass of the He donor star andthe initial orbital period for SNe Ia increase with metallicity, while theminimum initial mass of the carbon--oxygen white dwarfs producing SNe Iadecreases with metallicity. For a constant star-formation galaxy, SN Iabirthrates increase with metallicity. If a single starburst is assumed, SNe Iaoccur systemically earlier and the peak value of the birthrate is larger for ahigh Z, and the He star donor channel with different metallicities can producethe young SNe Ia with delay times $\sim$45-220Myr.

The helium star donor channel for the progenitors of type Ia supernovae with different metallicities