In this paper, we study {bf twisted Milnor hypersurfaces} and compute their $hat A$-genus and Atiyah-Singer-Milnor $alpha$-invariant. Our tool to compute the $alpha$-invariant is Zhangs analytic Rokhlin congruence formula. We also give some applications about group actions and metrics of positive scalar curvature on twisted Milnor hypersurfaces.
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