II. (50 points) On an infinite grid paper, some cells are colored red, and the rest are colored blue. In every $2 \times 3$ rectangle of six cells, there are exactly two red cells. How many red cells are there in a $9 \times 11$ rectangle of 99 cells?
II. 33 Red Squares.
As shown in Figure 3, take any red square $K_{0}$ as the center of a $3 \times 3$ square; it is not allowed to color $K$ red. If $K$ is colored red, then in the $2 \times 3$ rectangles $A F H D$, $A B S T$, and $M N C D$, there will be two red squares each. To ensure that the shape $B C G E$ contains two red squares, no matter where the red square is placed, it will result in one of the aforementioned three rectangles having 3 red squares. This means that the red square cannot share a side with $K_{0}$, but must be on its diagonal. This is feasible overall (as shown in Figure 4).

Therefore, each $3 \times 3$ square contains exactly 3 red squares.

Furthermore, in a $9 \times 11$ rectangle, it can be divided into nine $3 \times 3$ squares and three $2 \times 3$ rectangles, so there are a total of $9 \times 3 + 3 \times 2 = 33$ red squares.