  The asymptotic formula of the number of integral points in non-compact
symmetric homogeneous spaces of semi-simple simply connected algebraic groups
is given by the average of the product of the number of local solutions twisted
by the Brauer-Manin obstruction. The similar result is also true for
homogeneous spaces of reductive groups with some restriction. As application,
we will give the explicit asymptotic formulae of the number of integral points
of certain norm equations and explain that the asymptotic formula of the number
of integral points in Theorem 1.1 of \cite{EMS} is equal to the product of
local integral solutions over all primes and answer a question raised by
Borovoi related to the example 6.3 in \cite{BR95}.
