Elliptic points of the Drinfeld modular groups

Let $K$ be an algebraic function field with constant field ${mathbb F}_q$. Fix a place $infty$ of $K$ of degree $delta$ and let $A$ be the ring of elements of $K$ that are integral outside $infty$. We give an explicit description of the elliptic points for the action of the Drinfeld modular group $G=GL_2(A)$ on the Drinfelds upper half-plane $Omega$ and on the Drinfeld modular curve $G!setminus!Omega$. It is known that under the {it building map} elliptic points are mapped onto vertices of the {it Bruhat-Tits tree} of $G$. We show how such vertices can be determined by a simple condition on their stabilizers. Finally for the special case $delta=1$ we obtain from this a surprising free product decomposition for $PGL_2(A)$.