MVC doesn't allow to define it, C# does. Just because some construct is possible in the programming language, doesn't mean that your framework will support it. There are many other things that are possible to write in C#, but which MVC will ignore or complain about.
So, no, no static actions. No extension methods either. Extension methods are just a syntax sugar; a sleight of hand by the C# compiler. When the code gets compiled, the extension methods become no different than any other static methods. Calls to them are converted to simple static method calls. In other words, even if you write this:
myObject.extensionMethod(42);
It will get compiled to this:
ExtensionClass.extensionMethod(myObject, 42);
So by the time your application is run and MVC framework kicks in, all information about any extension methods is lost. MVC couldn't support "extension method actions" even if it wanted to, because it couldn't figure out which extension methods apply to which controller class.
