Regarding to management of a multi-task IT project;
How to deal with technical group manager who risks the completion of the project in time by not respecting weekly work-schedule?
What you can do:
Deal with the risk first: you have identified a clear problem impacting your project so if you haven't done so, formalize risk identification and qualification through your controlling processes/mechanisms (e.g. record the risk in the risk log, evaluate impact/likelihood, assign it to the technical group manager and communicate to the relevant people). Address the risk with the group manager to verify (s)he is aware of it, its impact and what his/her options are to mitigate it (more time, budget, resources, technical knowledge, etc.?), what kind of support (s)he needs.
Keep it neutral and factual: especially if you are an external resource managing the project with inhouse project team members, you need to be careful not to antagonise or alienate the latter. Keep the problem management to facts: what the problem is, how it affects the project, how to resolve it. Try not to make it a "I have problem with this person" kind of things.
Escalate the problem: if the group manager is not willing to address the risk and you don't have authority over him/her, you need to escalate it through your decision-making channels (e.g. your boss or your project sponsor) so that people with the appropriate authority level can help resolve the problem. Keep the group manager in the loop though - again, stick to facts, stay away from making it a personal thing and follow your process.
"...not respecting the weekly work schedule" implies a malicious intent by this group manager. Is that true or is he unable to comply with the schedule. If the latter, was he part of the estimating, planning, and scheduling process? If the former, does he have buy-in with the project itself?
Angeline offers great advice, but on top of this, if he was not part of the scheduling process as he should have been, do not hesitate in returning to the planning process and establishing a new schedule with his input and buy-in this time, go through the process change control process and cut a second baseline.
It is not rare for someone to maliciously sabotage a project with which they do not agree; however, my dollars are on the fact the he cannot meet the schedule given his other priorities. Rescheduling is a bit more win-win in this situation, IMO.