What would you do if one of your students refuse to do an activity with the rest of the group?

I appriciate the question as I feel it essential to discuss and as challenging important to deal with. First thing to deal with this is to know the reason behind the refusal. Take feedback. Know the likes and dislikes about the activity and accordingly assign his/her role/contribution. If nothing works out, ask the person to lead/manage/monitor others and would be accountable to team performance. 

Well it is so simple, you have to apply what we call the differentiated pedagogy

Take a good one to one meeting with him or her . That's the only solution to it. If an employee or subordinate refuses to work with the team then he or she is lacking team spirit so they need to be clearly communicated on these lines.

I would talk to the student to try and identify the reason why he/she does not want to participate in the group activity. I would also try to explain the importance of team work and try to highlight how fun and interesting it could be. I would also give the student support by not forcing them to participate but encouraging them by being with them through the activity to boost their confidence. The key is making the student feel understood and listened to. Acknowledging them while still encouraging them.

The refusal will surely have a reason...the teacher needs to identify the reason by talking to the student and analyze the situation.The reason can vary amongst, being shy of opposite gender, having low self confidence, may not like a member of the group, have less or no knowledge of the activity in question or any personal reason.Once the cause is identified its easier to cope up...the teacher may try options like changing the group etc.However a continual effort is needed by the teacher to include the student in the group activity.Topics like Working with others can also be discussed in the class.

Yes, I will give him the opportunity to work alone and then meet with him and try to get to what is upset with the group and give him lessons in the spirit of brotherhood and collective activity and motivation

By making a comparison between the results of team work activity and the result of one member activity, With open discussion and highlights the positive results of team work.