The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves

We study the integral Chow ring of the stack H₆, ₍ parametrizing n-pointed smooth hyperelliptic curves of genus g. We compute the integral Chow ring of H₆, ₍ for n=1, 2 completely, while for 3 n2g+2 we compute it up to the additive order of a single class in degree 2. We obtain partial results also for n=2g+3. In particular, taking g=2 and recalling that H₂, ₍=M₂, ₍, our results hold for CH^* (M₂, ₍) for 1 n7.