Steady Gradient Ricci Solitons with $O(p)\times O(q)$ Symmetry

We find new examples of steady gradient Ricci solitons with positive curvature operator in dimensions four and above. Utilising a procedure first introduced by Lai, we construct examples with $O(p)\times O(q)$ symmetry in dimension $p+q$ for any pair of integers $p,q\ge 2$ and discuss their asymptotic geometry.