C# "your" cursor in a window?

Question

Windows

Is it actually possible to make a separate, independent cursor from the main one that works only in the program window and could be controlled programmatically? For example, as it is done in VirtualBox.
Namely, how in VirtualBox when mouse capture is supported, we go outside the program, and the cursor remains in its place, and inside the program we can use its separate copy regardless of the main one? - can this be done?