  Let $(A,\mathfrak{m})$ be a Henselian Cohen-Macaulay local ring and let CM(A)
be the category of maximal Cohen-Macaulay $A$-modules. We construct $T \colon
CM(A)\times CM(A) \rightarrow mod(A)$, a subfunctor of $Ext^1_A(-, -)$ and use
it to study properties of associated graded modules over $G(A) =
\bigoplus_{n\geq 0} \mathfrak{m}^n/\mathfrak{m}^{n+1}$, the associated graded
ring of $A$. As an application we give several examples of complete
Cohen-Macaulay local rings $A$ with $G(A)$ Cohen-Macaulay and having distinct
indecomposable maximal Cohen-Macaulay modules $M_n$ with $G(M_n)$
Cohen-Macaulay and the set $\{e(M_n)\}$ bounded (here $e(M)$ denotes
multiplicity of $M$).
