A generalization of the orthogonality relations of Green functions (Q1320062)

Let \(G\) be a reductive algebraic group \(G\) with an automorphism \({\mathfrak o}\) of order 2 over a finite field \(\mathbb{F}_ q\) and \({\mathfrak p}\) be the \(+1\)-eigenspace of \({\mathfrak o}\) in the Lie algebra. The author determines (under some mild restrictions) the sum of a Deligne-Lusztig character over the rational points of the global analogue of \({\mathfrak p}\).