  Using the Langlands-Kottwitz paradigm, we compute the trace of Frobenius
composed with Hecke operators on the cohomology of nearby cycles, at places of
parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas.
Following an argument of Ngo, we then use this to give a geometric proof of a
base change fundamental lemma for parahoric Hecke algebras for GL_n over local
function fields. This generalizes a theorem of Ngo, who proved the base change
fundamental lemma for spherical Hecke algebras for GL_n over local function
fields, and extends to positive characteristic (for GL_n) a fundamental lemma
originally introduced and proved by Haines for p-adic local fields.
