The classical Satake isomorphism implies that the spherical Hecke algebra for GLn(Qp) is isomorphic to the ring of symmetric Laurent polynomials in n variables. Under the unramified local Langlands corre- spondence, one can view these polynomials as functions on the set of un- ramified L-parameters; each polynomial takes an unramified L-parameter to its evaluation at n-tuple of the Frobenius eigenvalues. In the context of the categorical local Langlands correspondence, we get an isomorphism between the spherical Hecke algebra and the ring of global functions on the moduli space of unramified L-parameters. In this talk, I will discuss p-adic and mod p analogues of this statement, where the space of unrami- fied L-parameters are replaced by certain loci in the moduli stack of etale (φ,Γ)-modules (so-called the Emerton-Gee stack). If time permits, I will discuss the connection with the categorical p-adic local Langlands program.