  For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds
that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of
these manifolds has hyperbolic intersection form and is stably parallelisable.
In fact we construct infinitely many such infinite sets. To achieve this we
prove a realisation result for appropriate subsets of Kreck's modified surgery
monoid $\ell_{2q+1}(\mathbb{Z}[\pi])$, analogous to Wall's realisation of the
odd-dimensional surgery obstruction $L$-group $L_{2q+1}^s(\mathbb{Z}[\pi])$.
