  We consider the index problem of certain boundary groupoids of the form
$\mathcal{G} = M _0 \times M _0 \cup \mathbb{R}^q \times M _1 \times M _1$.
Since it has been shown that for the case that $q \geq 3$ is odd, $K _0 (C^*
(\mathcal{G})) \cong \bbZ $, and moreover the $K$-theoretic index coincides
with the Fredholm index, we attempt in this paper to derive a numerical formula
for elliptic differential operators on $\mathcal{G}$. Our approach is similar
to that of renormalized trace of Moroianu and Nistor \cite{Nistor;Hom2}.
However, we find that when $q \geq 3$, the eta term vanishes, and hence the
$K$-theoretic and Fredholm indices of elliptic (respectively fully elliptic)
pseudo-differential operators on these groupoids are given only by the
Atiyah-Singer term. As for the $q=1$ case we find that the result depends on
how the singularity set $M_1$ lies in $M$.
