Let $R$ be an affine $\mathbb C-$algebra with a linear involution $x\rightarrow \bar x=\iota(x)$, let $S=R/\iota$ and $\psi:R^n\times R^n\rightarrow R$ be an $R/S-$hermitian form. Finaly let $$SU_n(R)=\{\phi\in SL_r(R)| \psi(\phi\times\phi)=\psi\}$$
Then $SU_n(R)$ has the structure of an ind-scheme over $\mathbb C$.
How can one prove that $SU_n(R)$ is integral ?
