A question concerning the Cellular Algebra, which is why $(P\otimes_AC^{\mu\star})\otimes_RC^\mu\cong(\dim P\otimes_AC^{\mu\star})C^\mu$?

Question

Let $A$ be a Cellular Algebra over the integral domain $R$.

Let $C^{\mu\star}$ be a left $A$-module and $C^\mu$ be a right $A$-module.

Let $P=Ae$ be a principal indecomposable $A$-module.

What confused me is why "$(P\otimes_AC^{\mu\star})\otimes_RC^\mu\cong(dimP\otimes_AC^{\mu\star})C^\mu$"?

This question is in line 7 of page 14 of the paper "Iwahori-Hecke Algebras and schur Algebras of the symmetric group"..

Thanks to everyone!