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