my twelve year old grandson will not behave

You may need professional help. Have you spoken to his school? If he's giving cause for concern there too then he may need to be referred to the Educational Pyschologist. I've worked with some who are excellent and others I'd not leave my cat with for a weekend, so you'll need to pass any recommendations they might make through your own reality checker.
If it's not sufficiently severe to refer to an Ed. Pysch then perhaps you need to firstly talk to him and see if he'll open up. Being away from his mother can be stressful. And if you can together set a few realistic boundaries which are rewarded not with costly rewards but extras such as staying up longer, his favourite dinner, etc. and not every good deed needs a reward, sometimes a cuddle, if he'll let you, a high five, a verbal 'well done' will suffice for the little things. Also remind him that you love him often, he might be testing your love in his own 12-year old way.

Poor lad must be very confused. He will think no one loves him. Perhaps the only way he has been able to get attention is to misbehave? Changing at this age will not be quick and will need a lot of love and patience. I agree with all Aka has said and would add that perhaps deprivation of privileges might also help? Perhaps you could say, if you do such and such again you won't be allowed to ........................?

That sounds really challenging sheila01 and I agree you need professional help. I suggest you make an appointment to meet with his head of year/head of house as soon as possible and try to enlist their help. I assume they know he has had problems at home - if not, it would help them to be in the picture and they are the people who can bring in professional help from local services.

Yes, the school is the starting place and the visiting educational pychologist can gen up on what is known so far, then talk with you and the teachers about what might be a useful way forward. You might find his behaviour differs according to where he is. Can you find any time for the two of you to do something enjoyable together? Maybe an outing, picnic, visit somewhere special that he can look forward to?

Who is he with in the evening and at weekends when you are working? Can they shed any light on his behaviour?

sheila01, my own 13-year-old grand-daughter's behaviour at home is really very bad. At school, where she's doing really well, her behaviour is perfect, and the teachers aren't at all aware of how things are at home.
If you feel you can speak to the teaching staff (would you need to let your daughter know this - is she available to talk to just now?)then I would try to do so. Perhaps the school aren't completely aware of any on-going issues at your grandson's home.
My son-in-law has decided that they will sort the problem themselves, with no involvement from outsiders. My daughter isn't at all happy about this, as she feels it's all gone too far, and her own relationship with my grand-daughter has completely broken down - and is very likely irretrievable.
If you can avoid any further problems for your grandson, by keeping the relevant staff informed, and with their advice, perhaps involving outside agencies such as educational psychologists, then it would more than likely really help him. I feel as if my own hands are tied, but you have this chance to help the young lad. Good luck.

All the advice already given is good. Until very recently I worked with disaffected teenagers and know how challenging their behaviour can be for carers. However, it is often a sign of unhappiness and low self-esteem; this is far more common than people realise, particularly if the challenging behaviour presents as verbally or physically aggressive.
Sanctions can be difficult to enforce and so the best way is what you have been doing - rewards. Now, as has been pointed out, rewards can take many forms. Breakfast in bed, after a weekend lie-in, is often a winner. Keep a tally, (not a sticker chart, uncool!) and agree that if 'x' amount of small rewards achieved then a bigger reward will be given. Don't time limit this as setbacks are common and the big reward needs to remain in sight.
The most important thing you can do is to find one positive thing each day to praise your grandson for. It can be any small thing but make it personal eg 'that was thoughtful, kind, generous, clever' or 'that t shirt really suits you'. You need to stick to this, every day, even if there has been an upset of sorts, find something good.
Avoid conflict, I would rather take a cup of tea in bed than spend more energy arguing. Teenagers need sleep and don't like mornings - fact. Try to make a good start to the day. Encourage eating breakfast and also any sport, just a kick about on the park or, if funds allow, join a club - running is cheap, archery is not. Contact the Youth Service to see what they can offer over the holidays, possibly Music/DJ mixing, trips out and sporty stuff.
Encourage Mum to adopt the same strategies and ask if she can help to fund rewards.
Good Luck, it won't always be like this and remember, your grandson is suffering too.

School is def the place to start. What's his behaviour like there? Have they noticed if anything triggers him? Have you noticed if anything triggers him? Is he taller, shorter, fatter, thinner, brighter, less bright, different in any way to his peers?

Avoid confrontation but set boundaries. Try not to back him into a corner...always try to leave him a face saving escape route. Involve him in the boundary setting if possible and in the rewards/consequences. Don't let the rewards turn into a money pit. A reward could be watching a movie together...it shouldn't be expensive. However at his age you could use money as a reward in order to save for something expensive. So when he has enough money he not only has the pleasure of buying the item but the satisfaction of knowing that he earned and saved the money. Consequences need to hurt but not hurt too much. Maybe no computer games for a set time. Grounding should be saved for the most serious offences.

That's excellent advice, caramac. I especially like the idea of saying something positive each day.