Kirill Zaynullin (Ottawa): This is a joint work with Rui Xiong and Changlong Zhong. Recently, Zhong found a realization of the oriented cohomology of an affine Grassmannian as a generalized Peterson algebra. Using the language of duoidal categories we prove that the generalized Peterson algebra is, indeed, the $HH_0$ of the small torus equivariant oriented cohomology of the Kac-Moody complete flag. We also discuss a generalization of the Peterson conjecture: we show that the dual of the generalized Peterson algebra can be interpreted as a quantum oriented cohomology of a projective line.
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