  Let $\mathbf{k}$ be an algebraically closed field, let $\Lambda$ be a finite
dimensional $\mathbf{k}$-algebra, and let $\widehat{\Lambda}$ be the repetitive
algebra of $\Lambda$. For the stable category of finitely generated left
$\widehat{\Lambda}$-modules $\widehat{\Lambda}$-\underline{mod}, we show that
the irreducible morphisms fall into three canonical forms: (i) all the
component morphisms are split monomorphisms; (ii) all of them are split
epimorphisms; (iii) there is exactly one irreducible component. We next use
this fact in order to describe the shape of the Auslander-Reiten triangles in
$\widehat{\Lambda}$-\underline{mod}. We use the fact (and prove) that every
Auslander-Reiten triangle in $\widehat{\Lambda}$-\underline{mod} is induced
from an Auslander-Reiten sequence of finitely generated left
$\widehat{\Lambda}$-modules.
