Let $k$ be an algebraically closed field of characteristic zero and let $G$ be a non-connected linear algebraic group with reductive connected component $G^0$ over $k$. What is known about the semi-simple elements in $G$ ? Are they dense in every connected component of $G$ ? Do they contain an open dense subset of every connected component of $G$ ?

If $G$ is instead connected, then the answer is yes, as the regular semi-simple elements form an open dense subset. Also I am aware of a result of Guralnik and Malle [Lemma 6.9 in "Simple groups admit Beauville structures" J. Lond. Math. Soc. (2) 85 (2012), no. 3, 694-721] which gives the answer YES in a special case. Note that in characteristic zero all unipotent elements lie in $G^0$.

Let $k$ be an algebraically closed field of characteristic zero and let $G$ be a non-connected linear algebraic group with reductive connected component $G^0$ over $k$. What is known about the semi-simple elements in $G$ ? Are they dense in every connected component of $G$ ? Do they contain an open dense subset of every connected component of $G$ ?

If $G$ is instead connected, then the answer is yes, as the regular semi-simple elements form an open dense subset. Also I am aware of a result of Guralnick and Malle [Lemma 6.9 in "Simple groups admit Beauville structures" J. Lond. Math. Soc. (2) 85 (2012), no. 3, 694-721] which gives the answer YES in a special case. Note that in characteristic zero all unipotent elements lie in $G^0$.