Construct a generic type through reflection given the type of another object

I'm passing a type to a method and creating an object based on that type. Assume argType is a Type and passed to the method as a parameter.

var assembly = AppDomain.CurrentDomain.GetAssemblies().Single(a => a.GetName().Name == "MyAssembly");
var newType = assembly.GetTypes().SingleOrDefault(x => x.FullName == argType.FullName + "Suffix");
var newObject = Activator.CreateInstance(newType);

This works fine for most objects, but if I pass a type with a generic sub type (e.g. MyClass<MyType>), it fails [I'd need to create a MyClassSuffix<MyType>].

How could the code above be improved so that generic types (ending with "Suffix") can also be created? I looked at the FullName property for such types which contain substrings like '1[[. I'd rather not do regex parsing to append "Suffix" before these characters begin. I'm thinking there is a better way.