Let $G$ be a split connected reductive group over finite field of characteristic $p > 2$ such that $G_\text{der}$ is absolutely almost simple. We give geometric construction perverse $\mathbb{F}_p$-sheaves on the Iwahori affine flag variety which are central with respect to convolution product. deduce an explicit formula for isomorphism from spherical mod $p$ Hecke algebra center algebra. also ...