I know that when a program inside a Virtual Machine full virtualized tries to execute a privileged instruction,since it is running in user mode, the "trap and emulate" occurs and so the Hypervisor running in the host machine takes the control of the CPU and emulates the privileged instruction since the privileged instruction requires to be executed in system mode but all the code in a VM (applications and kernel) is executed in user mode.
I was wondering what happens with contenxt switch inside a the VM between for instance two processes after that a time interrupt occurs and the scheduler routine must be executed. The scheduler should not be executed in system mode?So does the hypervisor take the control each time there is a switch between two processes within the VM?