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We provide new examples of \'etale extensions of Green functors bytransferring classical examples of \'etale extensions to the equivariantsetting. Our examples are Tambara functors, and we prove Green \'etaleness forthem, which implies Tambara \'etaleness. We show that every $C_2$-Galoisextensions of fields gives rise to an \'etale extension of $C_2$-Greenfunctors. Here we associate the constant Tambara functor to the base field andthe fix-Tambara functor to the extension. We also prove that all $C_n$-Kummerextensions give rise to \'etale extensions for arbitrary finite $n$. \'Etaleextensions of fields induce \'etale extension of $G$-Green functors for anyfinite group $G$ by passing to the corresponding constant $G$-Tambara functors.

Examples of \'etale extensions of Green functors