Integrating Large AI Models (LAMs) into 6G mobile networks is a key enabler of the AI-Native Air Interface (AI-AI), where protocol intelligence must scale beyond handcrafted logic. This paper presents, to our knowledge, the first standards-compliant emulation of the Radio Resource Control (RRC) layer using a decoder-only LAM (LLAMA-class) fine-tuned with Low-Rank Adaptation (LoRA) on a multi-vendor corpus of real-world traces spanning both 5G and 4G systems. We treat RRC as a domain-specific language and construct a segmentation-safe, question-answer (Question-and-Answer (QA)) dataset that preserves Abstract Syntax Notation (ASN.1) structure through linearization prior to Byte Pair Encoding (BPE) tokenization. The proposed approach combines parameter-efficient adaptation with schema-bounded prompting to ensure syntactic and procedural fidelity. Evaluation introduces a standards-aware triad -- ASN.1 conformance, field-level coverage analysis, and uplink-to-downlink state-machine checks -- alongside semantic similarity and latency profiling across 120 configurations. On 30k 5G request-response pairs plus an additional 4.8k QA turns from 4G sessions, our 8B model achieves a median cosine similarity of 0.97, a 61% relative gain over a zero-shot baseline, while sustaining high conformance rates. These results demonstrate that LAMs, when augmented with protocol-aware reasoning, can directly orchestrate control-plane procedures, laying the foundation for the future Artificial Intelligence (AI)-native Radio Access Network (RAN).