Can you be "friends" with an ex of 4 years ?

So I have been dating him for about a year now. He had a 4+ yr relationship with his ex gf and in the beginning I was cool with them keeping in touch once in awhile. I tend to believe the best in people until they prove me otherwise. So about 5 months ago, my boyfriend was with me when he received 2 calls from his ex...she was calling him to "be on the phone while shes walking alone downtown after coming from a bar"....my question is WHY your ex?? Ok my boyfriend tells me how there is nothing going on between them and that she was "one of the guys" and shes the type of girl who you'd see around a group of guys. I tell him, look you wanted to marry this girl at one point...until she broke it off with you. SO after that night I told him how I felt about them meeting up to /catch up and even talk or text...any type of contact I didnt feel comfortable with it. Because she is showing signs that idk maybe she still has feelings? I can't trust her really, I barely know the girl. It just confuses me why my bf has strung this out and answered her calls and texts even after I told him how i felt! She comes back to her hometown and contacts my bf 5+ times (phone and text) asking if he is out or asking if he wants to go to lunch with her brother and his girlfriend. WHY is she so quick to contact her EX?? I told him that if she doesnt know how I truly feel, shes going to keep contacting him. I just have heard horror stories about ex's getting involved in the relationship and feel like its all just baggage. Ex's should stay in the PAST...right??? I am not crazy here. I am the most understanding patient girl my boyfriend has ever been with. Its annoying to hear my bf say "She texted me 3 times asking to come out" SHould HE get this dealt with? Or should I step in?? I want him to WANT to do this....but im not convicned he doesnt want to cut the ties for a reason he isnt telling me...

I am never one to say that people cannot be friends after they date because it isn't always true. Sometimes exes actually can be friends. The only catch is, you either really loved them and still do or you had love for them but it's something that can die off whenever. You said that he dated her for four years. How long was the break in between her and you? Also, is his ex single? The fact that she is the first one to call probably means that she either has no one else to depend on, she still has feelings for him, or that she knows that he will be there whenever she needs or wants him to be. Also, if he hasn't told her to not call so much or that she is overstepping the boundaries of what it means to be an ex... (With the exception of emergencies, then again there is a such thing as calling the authorities) then he is in the wrong also and probably enjoys the attention OR still has feelings for her too. DO NOT STEP IN.... well meaning do not deal directly with her. You will end up being the crazy girlfriend because she undoubtedly will piss you off. One big thing you are just going to have to accept is that he will more than likely not want to do this. You probably wouldn't want to either. Yet, some people do see that it is not worth losing what they have for something so silly. That is the big thing. Talk to him show him what you see and what he has told you. If you don't mind them being friends, tell him that there needs to be certain boundaries. If you just don't like it, tell him it makes you feel uncomfortable. P.S. I will be honest about this. Talking to him bluntly could go very good or very bad. You may fight or you won't fight and it goes smoothly... Still, you can't force a decision on him. All you can do is present what you see. Back it up with evidence. And tell him where you are coming from with it.