  We introduce a dimension group for a self-similar map as the ${\rm
K}_0$-group of the core of the $C^*$-algebra associated with the self-similar
map together with the canonical endomorphism. The key step for the computation
is an explicit description of the core as the inductive limit using their
matrix representations over the coefficient algebra, which can be described
explicitly by the singularity structure of branched points. We compute that the
dimension group for the tent map is isomorphic to the countably generated free
abelian group ${\mathbb Z}^{\infty}\cong {\mathbb Z}[t]$ together with the
unilatral shift, i.e. the multiplication map by $t$ as an abstract group. Thus
the canonical endomorphisms on the ${\rm K}_0$-groups are not automorphisms in
geneal. This is a different point compared with dimension groups for
topological Markov shifts. We can count the singularity structure in the
dimension groups.
