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  1. Let $$F$$ be a non-archimedean local field of residual characteristic $$p \neq 2$$ . Let $$G$$ be a (connected) reductive group over $$F$$ that splits over a tamely ramified field extension of $$F$$ . We revisit Yu's construction of smooth complex representations of $G(F)$ from a slightly different perspective and provide a proof that the resulting representations are supercuspidal. We also provide a counterexample to Proposition 14.1 and Theorem 14.2 in Yu [ Construction of tame supercuspidal representations , J. Amer. Math. Soc. 14 (2001), 579–622], whose proofs relied on a typo in a reference. 
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