Let $K$ be a field and $G$ a connected reductive group over $K$. Can we describe $K[G]^{*}$?
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6$\begingroup$ Up to multiplying by a scalar, any invertible function is a character, see math.stanford.edu/~conrad/papers/unitthm.pdf $\endgroup$– SashaPCommented Sep 16, 2019 at 21:00
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