Inclusion Criteria:
* Patient aged of 18 years or older,
* Patients with relapsing granulomatosis with polyangiitis positive for PR3-ANCA at inclusion according to the ACR/EULAR 2022 classification criteria, and/or the 2012 revised Chapel Hill Consensus Conference definition.
* Patients with an active disease defined as a Birmingham Vasculitis Activity Score (BVAS) ≥ 3,
* Patients within the first 21 days following initiation/increase of glucocorticoids at a dose ≤1 mg/kg/day (pulses of methylprednisolone before oral glucocorticoid therapy are authorized)
* Patient able to give written informed consent prior to participation in the study, - Affiliation with a mode of social security (profit or being entitled).
Exclusion Criteria
* Patients with MPO-positive AAV, or other vasculitis, defined by the ACR criteria and/or the Chapel Hill Consensus Conference,
* Patients with vasculitis in remission of the disease defined as a BVAS \< 3,
* Patients with a newly-diagnosis of GPA
* Patients treated with rituximab within the last 6 months before inclusion
* Patients treated with cyclophosphamide within the last 6 months before inclusion
* Patients with severe cardiac failure defined as class IV in New York Heart Association
* Subject known to be seropositive for human immunodeficiency virus (HIV), hepatitis B (included history of previous infection) or hepatitis C
* Patients with active cancer or recent cancer (\< 5 years), except basocellular carcinoma and prostatic cancer of low activity controlled by hormonal treatment,
* Patients with hypersensitivity to a monoclonal antibody or biologic agent,
* Patients with hypersensitivity to obinutuzumab or to its excipients
* Contra-indications to auxiliary medicinal products (methylprednisolone, paracetamol, prednisone, dexchlorpheniramine)
* Patients with other uncontrolled diseases, including drug or alcohol abuse, active infections or antecedents of chronic or recurrent infections, severe psychiatric diseases, that could interfere with participation in the trial according to the protocol,
* Patients suspected not to be observant to the proposed treatments,
* Pregnant women and lactation. All women of childbearing potential (WOCBP) are required to have a negative pregnancy test (blood or urine) before treatment and must agree to maintain highly effective contraception by practicing abstinence or by using an effective method of birth control from the date of consent through the end of the study, and at least 18 months after stopping obinutuzumab such as combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation (Oral, Intravaginal, Transdermal); Progestogen-only hormonal contraception associated with inhibition of ovulation (Oral, Injectable, Implantable); Intrauterine device (IUD); Intrauterine hormone-releasing system (IUS); Bilateral tubal occlusion; Vasectomised partner,
* Men who refuse to use effective method of contraception (condom) from the date of consent through the end of the study and at least 18 months after stopping obinutuzumab (unless permanently sterile by bilateral orchidectomy or vasectomy),
* Patient participating in another investigational therapeutic study
* Protected adults (including individual under legal guardianship by court order or curatorship) or adults deprived of liberty
* Patients unable to give written informed consent prior to participation in the study.
* Patients with severe liver insufficiency (prothrombin time \<50% and total bilirubin \>50 micrmol/L)) or pulmonary insufficiency requiring nasal oxygen,
* Patients with an active infection or a history of chronic or recurrent infections
* Vaccination with live virus vaccines in the 4 weeks before study enrolment
