Projections as convex combinations of surjective isometries on C(Ω)

We study properties of operators that are in the convex hull of a finite set of surjective isometries on the Banach space of complex valued continuous maps defined on a compact and connected topological space. We characterize those projections that are in the convex combination of two surjective isometries and we show that they are generalized bi-circular projections.