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We construct twisted Calogero-Moser (CM) systems with spins as the Hitchinsystems derived from the Higgs bundles over elliptic curves, where transitionsoperators are defined by an arbitrary finite order automorphisms of theunderlying Lie algebras. In this way we obtain the spin generalization of thetwisted D'Hoker- Phong and Bordner-Corrigan-Sasaki-Takasaki systems. As byproduct, we construct the corresponding twisted classical dynamical r-matricesand Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms ofthe Lie algebras.

Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems and KZB equations