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The results of the microscopic transport calculations of -nucleus interactions within a GiBUU model are presented. The dominating mechanism of hyperon production is the strangeness exchange processes → γπ and → ΞK. The calculated rapidity spectra of Ξ hyperons are significantly shifted to forward rapidities with respect to the spectra of S = −1 hyperons. We argue that this shift should be a sensitive test for the possible exotic mechanisms of -nucleus annihilation. The production of the double Λ-hypernuclei by Ξ− interaction with a secondary target is calculated.