  This is the third paper of a series (started by arXiv:0711.2083,
arXiv:0908.3390) 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 and affine
Zastava.
