Connected sums with HPn or CaP2 and the Yamabe invariant

Denoting the Yamabe invariant of a manifold X by Y(X), we show that if Y(M)≤0≤Y(HPkטF) and |Y(HPkטF)|+|Y(M)|≠0, thenY(M)=Y(M♯F(HPkטF)), where ♯F denotes a generalized connected sum along F. Likewise for the Cayley plane CaP2 when k=4. These results are used to produce examples of higher-dimensional manifolds with nonpositive Yamabe invariants.