  An exoflop occurs in the gauged linear $\sigma$-model by varying the Kahler
form so that a subspace appears to shrink to a point and then reemerge
"outside" the original manifold. This occurs for K3 surfaces where a rational
curve is "flopped" from inside to outside the K3 surface. We see that whether a
rational curve contracts to an orbifold phase or an exoflop depends on whether
this curve is a line or conic. We study how the D-brane category of the smooth
K3 surface is described by the exoflop and, in particular, find the location of
a massless D-brane in the exoflop limit. We relate exoflops to noncommutative
resolutions.
