  Twisted ind-Grassmannians are ind-varieties $\GG$ obtained as direct limits
of Grassmannians $G(r_m,V^{r_m})$, for $m\in\ZZ_{>0}$, under embeddings
$\phi_m:G(r_m,V^{r_m})\to G(r_{m+1}, V^{r_{m+1}})$ of degree greater than one.
It has been conjectured in \cite{PT} and \cite{DP} that any vector bundle of
finite rank on a twisted ind-Grassmannian is trivial. We prove this conjecture
under the assumption that the ind-Grassmannian $\GG$ is sufficiently twisted,
i.e. that $\lim_{m\to\infty}\frac{r_m}{\deg \phi_1...\deg\phi_m}=0$.
