  The use of improved staggered actions (HYP, Asqtad) has been proved to reduce
the scaling corrections that affected previous calculations of B_K with
unimproved (standard) staggered fermions in the quenched approximation. This
improved behaviour allows us to perform a reliable calculation of B_K including
quark vacuum polarization effects, using the MILC configurations with n_f=2+1
flavours of sea fermions. We perform such a calculation for a single lattice
spacing, a=0.125 fm, and with kaons made up of degenerate quarks with m_s/2.
The valence strange quark mass m_s is fixed to its physical value and we use
two different values of the light sea quark masses. After a chiral
extrapolation of the results to the physical value of the sea quark masses, we
find \hat B_K = 0.83+-0.18, where the error is dominated by the uncertainty in
the lattice to continuum matching at O(\alpha_s^2). The matching will need to
be improved to get the precision needed to make full use of the experimental
data on \epsilon_K to constrain the unitarity triangle.
