  We study the space of Riemannian metrics with positive scalar curvature on a
compact manifold with boundary. These metrics extend a fixed boundary metric
and take a product structure on a collar neighbourhood of the boundary. We show
that the weak homotopy type of this space is preserved by certain surgeries on
the boundary in co-dimension at least three. Thus, there is a weak homotopy
equivalence between the space of such metrics on a simply connected spin
manifold $W$, of dimension $n\geq 6$ and with simply connected boundary, and
the corresponding space of metrics of positive scalar curvature on the standard
disk $D^{n}$. Indeed, for certain boundary metrics, this space is weakly
homotopy equivalent to the space of all metrics of positive scalar curvature on
the standard sphere $S^{n}$. Finally, we prove analogous results for the more
general space where the boundary metric is left unfixed.
