Tilting objects in the stable category of vector bundles on a weighted projective line of type (2,2,2,2;λ)(2,2,2,2;λ)

We construct a tilting object for the stable category of vector bundles on a weighted projective line XX of type (2,2,2,2;λ)(2,2,2,2;λ). This consists of five rank-two bundles and one rank-three bundle whose endomorphism algebra is the canonical algebra associated with XX of type (2,2,2,2)(2,2,2,2).