  Let $G$ be an almost simple simply connected complex Lie group, and let
$G/U_-$ be its base affine space. In this paper we formulate a conjecture,
which provides a new geometric interpretation of the Macdonald polynomials
associated to $G$ via perverse coherent sheaves on the scheme of formal arcs in
the affinization of $G/U_-$. We prove our conjecture for $G=SL(N)$ using the so
called Laumon resolution of the space of quasi-maps (using this resolution one
can reformulate the statement so that only "usual" (not perverse) coherent
sheaves are used). In the course of the proof we also give a $K$-theoretic
version of the main result of arXiv/0811.4454.
