Examples of étale extensions of Green functors

We provide new examples of étale extensions of Green functors by transferring classical examples of étale extensions to the equivariant setting. Our examples are Tambara functors, and we prove Green étaleness for them, which implies Tambara étaleness. We show that every $C_2$-Galois extensions of fields gives rise to an étale extension of $C_2$-Green functors. Here we associate the constant Tambara functor to the base field and the fix-Tambara functor to the extension. We also prove that all $C_n$-Kummer extensions give rise to étale extensions for arbitrary finite $n$. Étale extensions of fields induce étale extension of $G$-Green functors for any finite group $G$ by passing to the corresponding constant $G$-Tambara functors.