According to FIFA rules, a player is allowed to perform a certain degree of hesitation or stutter step during their run-up to a penalty kick. However, there are specific limitations to prevent unfair advantage:

Key Points from FIFA's Laws of the Game (Law 14 - The Penalty Kick):
Feinting during the run-up: Players are allowed to feint or hesitate during their approach to take a penalty kick. This means they can slow down, stutter step, or change pace as they approach the ball.

Feinting once at the ball: Players are not allowed to feint once they have completed their run-up and are about to kick the ball. Specifically, a player cannot stop completely or significantly delay their kick once their kicking motion has begun. This is considered unsporting behavior.

Consequences of Violations:
If the kicker feints after completing the run-up (before or during the kick): The referee will consider this an infringement. The outcome depends on whether the ball goes into the goal or not:
If the ball enters the goal: The kick is retaken, and the player may receive a caution (yellow card) for unsporting behavior.
If the ball does not enter the goal: An indirect free kick is awarded to the defending team from the spot where the infringement occurred.
In summary, while players can hesitate or stutter step during their run-up to a penalty kick, they must not feint or hesitate once they have completed their run-up and are about to kick the ball. Violation of this rule results in the penalty kick being retaken or an indirect free kick awarded to the opposing team.