The K(π, 1) problem for the affine Artin group of type (B)over-tilden and its cohomology

We prove that the complement to the affine complex arrangement of type (B) over tilde (n) is a K(pi, 1) space. We also compute the cohomology of the affine Artin group G (B) over tilde (n) ( of type (B) over tilde (n)) with coefficients in interesting local systems. In particular, we consider the module Q [q+/-1; t+/-1]; where the first n standard generators of G (B) over tilde (n) act by (-q)-multiplication while the last generator acts by (-t)-multiplication. Such a representation generalizes the analogous 1-parameter representation related to the bundle structure over the complement to the discriminant hypersurface, endowed with the monodromy action of the associated Milnor fibre. The cohomology of G (B) over tilde (n) with trivial coefficients is derived from the previous one.