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We formulate a conjecture on the motivic McKay correspondence for the groupscheme $ \alpha_{p}$ in characteristic $p>0$ and give a few evidences. Theconjecture especially claims that there would be a close relation betweenquotient varieties by $\alpha_{p}$ and ones by the cyclic group of order $p$.

Notes on the motivic McKay correspondence for the group scheme $\alpha_{p}$