When the game slows down, this is due to lag. If you are the home team, then you will experience no lag in the first half, lag in the second half, lag in the first period of extra time, and no lag in the last period. If you are the away team, then vice versa. Lag itself is a part of the online experience, and it's very possible that your opponent isn't cheating.
However, people do sometimes cheat by taking advantage of the lag situation. What people do very often to cheat (don't do this, it's lame!) is they will exacerbate the lag during their lag free halves. For instance, say they are the home team, during the first half they will download a bunch of stuff to slow down their connection. They do not experience a difference in gameplay, but you surely will. When the second half comes around, they stop downloading because it is their turn to experience the lag.
This problem is ubiquitous, although lag isn't as bad this year as last year. Once again, don't do this.
