If you are used to GNOME, then you are probably used to moving your window to a different Workspace (or Virtual Desktop) by using Ctrl+Alt+Shift+Arrow key. In KDE, this combination apparently is not part of the normal workflow. In fact, by default there is not even a key assignment to switch your view to a different Workspace. That second problem I solved by going into System Settings → Workspace Behavior → Virtual Desktops → Switching → Shortcuts. At the time that seemed like the obvious place to look for a solution for both of my problems, but sadly that was not the case.
The moving of windows is in fact hidden in another menu item. Opening System Settings again, we now pick Shortcuts and Gestures. In that window, pick the Global Keyboard Shortcuts tab and then switch the KDE component to KWin. Now there should be a long list of different options and most of them will not have any keys assigned to it. If you are up for even more customization, have a look at all the options, otherwise scroll down to Window One Desktop Down. This options and the three ones below it are the options that need changing to allow switching your windows across virtual desktops. You can choose your own, or just pick the ones that are also used in GNOME.
- Window One Desktop Down - Ctrl+Alt+Shift+↓
- Window One Desktop to the Left - Ctrl+Alt+Shift+←
- Window One Desktop to the Right - Ctrl+Alt+Shift+→
- Window One Desktop Up - Ctrl+Alt+Shift+↑
In retrospect it was in an obvious place, it just might be a bit confusing if you are new to KDE. For example, if you come across the switching desktops shortcuts in Workspace Behavior, you might also expect to find the moving of windows there and not expect to have to look for that elsewhere. All in all, it is not bad though. KDE is an amazing Desktop Environment, the myriad of options are more than welcome when you compare it to the recent evolution in Ubuntu’s Unity and GNOME (though GNOME is at least trying). With that in mind, it is only expected all the options have to be divided and again divided into smaller categories.