  In this paper we study weight homology of singular schemes. Weight homology
is an invariant of a singular scheme defined in terms of hypercoverings of
resolution of singularities. Our main result is McKay principle for weight
homology of quotient singularities, i.e. we describe weight homology of a
quotient scheme in terms of weight homology of an equivariant scheme. Our
method is to reduce the geometric McKay principle for weight homology to Kato's
cohomological Hasse principle for arithmetic schemes. The McKay principle for
weight homology implies McKay principle for the homotopy type of the dual
complex of the exceptional divisors of a resolution of a quotient singularity.
As a consequence we show that the dual complex is contractible for isolated
quotient singularities.
