Question regarding no of circular arrangements

I am reading about circular arrangements in this pdf on page 103. This is an image taken from that pdf 6.2. CIRCULAR PERMUTATIONS Proposition 6.2.15. Let $P_1, \ldots, P_n$ be all the arrangements of an m-multiset. Then, $$ [R_{0}+\cdots+R_{m-1}](P_{1}+\cdots+P_{n})=m(P_{1}+\cdots+P_{n}). $$ Let $P$ be an arrangement of an $m$-multiset with orbit size $k$. Then, by Proposition 6.2.10 $k$ divides $m$. Now, from the understanding obtained from the above example, we note that $[R_0 + \cdots + R_{m-1}](P)$ accounts for $\frac{m}{k}$ counts of the same circular arrangement, where $\frac{m}{k}$ is nothing but ‘the number of rotations fixing $P'$. Also, by Proposition 6.2.11, we know that two orbits are either disjoint or the same and hence the next two results are immediate. But I have trouble understanding the sentence "$(R_0 + \cdots + R_{m−1})(P)$ accounts for $\frac mk$ counts of the same circular arrangement" If we make all $m$ rotations of $P$ into circular arrangement don't we get $m$ counts of the same circular arrangement? Why only $\frac mk$? I understand there are $\frac mk$ counts of each distinct arrangement that gives the same circular arrangement. Example: If I have the arrangement $ABCABCABC$, On $R_1$ ,I get $BCABCABCA$ On $R_2$, I get $CABCABCAB$ On $R_3$, I get $ABCABCABC$ So if apply the rotations from $R_0$ to $R_8$, I get 3 of each. But all of them are referring to same circular arrangement, right? Or is my understanding incorrect?