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We provide some new computations of Farrell--Tate and Bredon (co)homology forarithmetic groups. For calculations of Farrell--Tate or Bredon homology, oneneeds cell complexes wherecell stabilizers fix their cells pointwise. Weprovide two algorithms computing an efficient subdivision of a complex toachieve this rigidity property. Applying these algorithms to available cellcomplexes for PSL4(Z) provides computations of Farrell--Tate cohomology forsmall primes as well as the Bredon homology for the classifying spaces ofproper actions with coefficients in the complex representation ring.

The Farrell--Tate and Bredon homology for PSL\_4(Z) via cell subdivisions