  Let $A$ be a diagonal linear operator on $\C^n$, with all eigenvalues
satisfying $0<|\alpha_i|<1$, and $M = (\C^n\backslash 0)/<A>$ the corresponding
Hopf manifold. We show that any stable holomorphic bundle on $M$ can be lifted
to a $G$-equivariant coherent sheaf on $\C^n$, where $G=(\C^*)^l$ is a Lie
group acting on $\C^n$ and containing $A$. This is used to show that all stable
bundles on $M$ are filtrable, that is, admit a filtration by a sequence $F_i$
of coherent sheaves, with all subquotients $F_i/F_{i-1}$ of rank 1.
