Hofer's question on intermediate symplectic capacities

Hofer asked (1989): if n >= 3 can the cylinder B-2 (1) x R2(n-1) be symplectically embedded into B (2(n-1))(R) x R-2 for some R > 0? We show that this is the case if R >= root 2(n-1) + 2(n-2) - 2. It follows that there are no intermediate symplectic capacities, between 1-capacities, first constructed by Gromov in 1985, and n-capacities like the volume. In 2008, Guth reached the same conclusion under the additional hypothesis that the intermediate capacities should satisfy the exhaustion property.