The orbital equivalence of Bernoulli actions and their Sinai factors

Given a countable amenable group <tex-math id="M1">{document}G{document}</tex-math> and <tex-math id="M2">{document}λ ∈ (0,1){document}</tex-math>, we give an elementary construction of a type-Ⅲ<tex-math id="M3">{document}λ{document}</tex-math> Bernoulli group action. In the case where <tex-math id="M4">{document}G{document}</tex-math> is the integers, we show that our nonsingular Bernoulli shifts have independent and identically distributed factors.