  We study the so-called averaging functors from the geometric Langlands
program in the setting of Fargues' program. This makes explicit certain cases
of the spectral action which was recently introduced by Fargues-Scholze in the
local Langlands program for $\mathrm{GL}_n$. Using these averaging functors, we
verify (without using local Langlands) that the Fargues-Scholze parameters
associated to supercuspidal modular representations of $\mathrm{GL}_2$ are
irreducible. We also attach to any irreducible $\ell$-adic Weil representation
of degree $n$ an Hecke eigensheaf on $\mathrm{Bun}_n$, and show, using the
local Langlands correspondence and recent results of Hansen and
Kaletha-Weinstein, that it satisfies most of the requirements of Fargues'
conjecture for $\mathrm{GL}_n$.
