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I know the definition of convolution product in D.Gaitsgory's paper, but I can give a convolution product

$p:G(K)\times Fl \to Fl\times Fl$,$q:G(K)\times Fl \to G(K)\times_{G(O)} Fl$, $m:G(K)\times_{G(O)} Fl \to Fl$

$A_1,A_2\in P_I (Fl)$,$A_1*A_2=Rm^* A$ ,$q^* A=p^*(A_1\times A_2)$

Does this definition coincide with the Gaitsgory's sense?

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    $\begingroup$ Gaitsgory has more than one paper, so it would be helpful if your reference were more precise. $\endgroup$
    – inkspot
    Commented Dec 14, 2011 at 20:15

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This has been defined in Gaitsgory's article "Construction of central elements in the affine Hecke algebra via nearby cycles" : http://arxiv.org/abs/math/9912074.

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