  The Hecke algebras and quantum group of affine type A admit geometric
realizations in terms of complete flags and partial flags over a local field,
respectively. Subsequently, it is demonstrated that the quantum group
associated to partial flag varieties of affine type C is a coideal subalgebra
of quantum group of affine type A. In this paper, we establish a lattice
presentation of the complete (partial) flag varieties of affine type D.
Additionally, we determine the structures of convolution algebra associated to
complete flag varieties of affine type D, which is isomorphic to the (extended)
affine Hecke algebra. We also show that there exists a monomial basis and a
canonical basis of the convolution algebra, and establish the positivity
properties of the canonical basis with respect to multiplication.
