  This is the second paper of a series (started by arXiv:0711.2083) which
describes a conjectural analog of the affine Grassmannian for affine Kac-Moody
groups (also known as the double affine Grassmannian). The current paper is
dedicated to describing a conjectural analog of the convolution diagram for the
double affine Grassmannian. In the case when G=SL(n) our conjectures can be
derived from arXiv:0809.2605.
