  Let $G$ be a reductive group, let $Gr=G((t))/G[[t]]$ be the corresponding
affine Grassmannian and let $Fl=G((t))/I$ be the affine flag variety. We
construct, following an idea of Belinson, a 1-parametric deformation of the
product $Gr\times G/B$ to $Fl$. We use this construction to produce perverse
sheaves on $Fl$ which are central with respect to the convolution product from
spherical perverse sheaves on $Gr$.
