  We present preliminary results at {\beta} = 1.95 (a = 0.077 fm) on the first
unquenched N_f=2+1+1 lattice computation of the B_K parameter which controls
the neutral kaon oscillations in the Standard Model. Using N_f=2+1+1 maximally
twisted sea quarks and Osterwalder-Seiler valence quarks we achieve O(a)
improvement and a continuum-like renormalization pattern for the four-fermion
operator. Our results are extrapolated/interpolated to the physical
light/strange quark mass but not yet to the continuum limit. The computation of
the relevant renormalization constants is performed non perturbatively in the
RI'-MOM scheme using dedicated simulations with N_f=4 degenerate sea quark
flavours produced by the ETM collaboration.
  We get B_K^{RGI} (a = 0.077) = 0.747(18), which when compared to our previous
unquenched N_f=2 determination and most of the existing results, suggests a
rather weak B_K^{RGI} dependence on the number of dynamical flavours. We are at
the moment analysing lattice data at two additional {\beta} values which will
allow us to perform an extrapolation to the continuum limit.
