  We establish formulae for the part due to torsion of the equivariant
K-homology of all the Bianchi groups (PSL\_2 of the imaginary quadratic
integers), in terms of elementary number-theoretic quantities. To achieve this,
we introduce a novel technique in the computation of Bredon homology:
representation ring splitting, which allows us to adapt the recent technique of
torsion subcomplex reduction from group homology to Bredon homology.
