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We establish restrictions on Lagrangian embeddings of rational homologyspheres into certain open symplectic manifolds, namely the (A_m) Milnor fibresof odd complex dimension. This relies on general considerations aboutequivariant objects in module categories (which may be applicable in othersituations as well), as well as results of Ishii-Uehara and Ishii-Ueda-Ueharaconcerning the derived categories of coherent sheaves on the resolutions of(A_m) surface singularities.

Lagrangian homology spheres in (A_m) Milnor fibres via C^*-equivariant A_infinity modules