jmc

We see that the largest power of 9 that is less than 2014 is $9^3=729$, and the largest multiple of 729 less than 2014 is 1458, or $2\cdot 729$. From here, we find that the largest power of nine less than $2014-1458=556$ is $9^2=81$, and the largest multiple of 81 less than 556 is 486, or $6\cdot 81$. Next, the largest power of nine that is less than $556-486=70$ is $9^1=9$, giving us 63 or $7\cdot 9$ as the largest multiple of 9. Finally, this leaves us with $70-63=7$, or $7\cdot 1=7\cdot 9^0$. Therefore, we can express 2014 as $2\cdot 9^3+6\cdot 9^2+7\cdot 9^1+7\cdot 9^0$, which gives us $\boxed{2677_9}$.