Abstract: It is well known that the affine Hecke algebra can be realized as functions on the p-adic group, or as equivariant K group of the Steinberg variety for the Langlands dual group. In this talk, I will compare the corresponding periodic modules for the affine Hecke algebra. On the K theory side, we have stable basis constructed by Maulik--Okounkov and the fixed point basis. These bases will be identified will the standard basis and the Casselman basis on the p-adic side. With this, we can have an equivariant K-theory interpretation for the Macdonald and Casselman--Shalika formulas. Joint work with G. Zhao and C. Zhong.