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Let $G$ be the Weil restriction of a general linear group. By extending themethod of semi-modules developed by de Jong, Oort, Viehmann and Hamacher, weobtain a stratification of the affine Deligne-Lusztig varieties for $G$ (in theaffine Grassmannian) attached to a minuscule coweight and a basic element. Asan application, we verify a conjecture by Chen and Zhu on irreduciblecomponents of affine Deligne-Lusztig varieties for $G$.

Semi-modules and irreducible components of affine Deligne-Lusztig varieties