The results of the microscopic transport calculations of $bar p$-nucleus interactions within a GiBUU model are presented. The dominating mechanism of hyperon production is the strangeness exchange processes $bar K N to Y pi$ and $bar K N to Xi K$. The calculated rapidity spectra of $Xi$ 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 $bar p$-nucleus annihilation. The production of the double $Lambda$-hypernuclei by $Xi^-$ interaction with a secondary target is calculated.
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