Here is my 2 cents:
Type genericType = typeof(Repository<>);
Type[] typeArgs = { Type.GetType("TypeRepository") };
Type repositoryType = genericType.MakeGenericType(typeArgs);
object repository = Activator.CreateInstance(repositoryType);
Answering the question in comment.
MethodInfo genericMethod = repositoryType.GetMethod("GetMeSomething");
MethidInfo closedMethod = genericMethod.MakeGenericMethod(typeof(Something));
closedMethod.Invoke(repository, new[] { "Query String" });