Let $X={\rm Gr}_{n,k,{\Bbb R}}$ denote the Grassmannian of $k$-dimensional subspaces in ${\Bbb R}^n$. We regard $X$ as an ${\Bbb R}$-variety with the set of complex points $X({\Bbb C})={\rm Gr}_{n,k,{\Bbb C}}$. We consider the twisted $\Bbb R$-forms $_c X$ of $X$ where $c\in {\rm Aut\,} X_{\Bbb C}$ is a $1$-cocycle. They have the following property: $({}_c X)\times_{\Bbb R}{\Bbb C}\simeq X\times_{\Bbb R}{\Bbb C}$.
Question 1. What are the twisted $\Bbb R$-forms $_c X$ of $X$ having ${\Bbb R}$-points?
Question 2. What are references for the version of Question 1 over an arbitrary field rather than over ${\Bbb R}$?
Concerning Question 1, I have found the following twisted forms $_c X$, for which I write the set of ${\Bbb R}$-points $({}_c X)({\Bbb R})$.
${\rm Gr}_{n,k,{\Bbb R}}.$
For $n=2n',\ k=2k'$, the quaternionic Grassmannian ${\rm Gr}_{n',k',{\Bbb H}}$ of $k'$-dimensional subspaces in ${\Bbb H}^{n'}$, where ${\Bbb H}$ denotes the division algebra of Hamilton's quaternions.
For $n=2k$, the isotropic Hermitian Grassmannian whose ${\Bbb R}$-points are the $k$-dimensional subspaces $W\subset{\Bbb C}^n={\Bbb C}^{2k}$ that are totally isotropic with respect to the Hermitian form $\mathcal H$ with matrix ${\rm diag}(-1,\dots,-1,+1,\dots, +1)$ where $-1$ appears $k$ times and also $+1$ appears $k$ times. Here a subspace $W\subset {\Bbb C}^{2k}$ is called totally isotropic if the restriction of $\mathcal H$ to $W$ is zero.
Question 3. Do these exhaust all twisted real forms of $X$ having real points?